Appendix
$$\begin{aligned} & \, A_{0,11} = R^{*} h^{*} { ; }A_{0,13} = h^{*} Z_{2} \theta_{1} { ; }A_{0,14} = R^{*} h^{*} \theta_{1} \left( {w_{10}^{*} + 1} \right){ ; }A_{0,21} = \frac{{\varepsilon h^{*} Z_{2} }}{4}\frac{{dh^{*} }}{{dx^{*} }}{ ; }A_{0,22} = - \, \frac{{5R^{*} \theta_{2} }}{6}{ ;} \\ \, & A_{0,24} = \frac{{\varepsilon h^{*2} }}{12}\left( {\frac{{3Z_{2} \theta_{1} }}{{h^{*} }}\frac{{dh^{*} }}{{dx^{*} }}\left( {w_{10}^{*} + 2} \right) - \frac{{10R^{*} \theta_{2} }}{{h^{*2} }}\frac{{dw_{00}^{*} }}{{dx^{*} }} + Z_{2} \left( {\theta_{1} - \frac{{5\theta_{2} }}{6}} \right)\frac{{dw_{10}^{*} }}{{dx^{*} }} + \frac{{5R^{*} \theta_{2} }}{6}} \right){ ; }A_{0,31} = - \frac{{\varepsilon^{2} R^{*} h^{*3} }}{12}\frac{{d^{2} w_{10}^{*} }}{{dx^{*2} }} + R^{*} h^{*} Z_{2} \theta_{1} { ;} \\ \, & A_{0,32} = - \frac{{5\varepsilon R^{*} h^{*} \theta_{2} }}{6}\left( {\frac{1}{{h^{*} }}\frac{d}{{dx^{*} }}\left( {R^{*} h^{*} } \right)\left( {w_{10}^{*} + 1} \right) + 2R^{*} \frac{{dw_{10}^{*} }}{{dx^{*} }}} \right){ ; }A_{0,33} = Z_{2}^{2} h^{*} , \\ & A_{0,34} = - \frac{{\varepsilon^{2} R^{*} h^{*3} }}{12}\left( \begin{aligned} \left( {\frac{{10R^{*} \theta_{2} }}{{h^{*2} }}\frac{{d^{2} w_{00}^{*} }}{{dx^{*2} }} + Z_{2} \theta_{1} \frac{{d^{2} w_{10}^{*} }}{{dx^{*2} }}} \right)\left( {w_{10}^{*} + 2} \right) + \frac{{30R^{*} \theta_{2} }}{{h^{*2} }}\left( {\frac{{dw_{00}^{*} }}{{dx^{*} }}\frac{{dw_{10}^{*} }}{{dx^{*} }}} \right) + \left( {\frac{{5\theta_{2} Z_{2} }}{{2h^{*} }}\frac{{dh^{*} }}{{dx^{*} }}\frac{{dw_{10}^{*} }}{{dx^{*} }}} \right)\left( {2w_{10}^{*} + 1} \right) + \hfill \\ \frac{{5Z_{2} \theta_{2} }}{2}\left( {\frac{{dw_{10}^{*} }}{{dx^{*} }}} \right)^{2} + \left( {\frac{20}{{h^{*3} }}\frac{d}{{dx^{*} }}(R^{*} h^{*} )\frac{{dw_{00}^{*} }}{{dx^{*} }} + \frac{{5Z_{2} }}{3}\frac{{d^{2} w_{10}^{*} }}{{dx^{*2} }}} \right)\left( {w_{10}^{*} + 1} \right)\theta_{2} + \frac{{10\theta_{2} }}{{R^{*} h^{*3} }}\left( {\frac{d}{{x^{*} }}\left( {R^{*} h^{*} } \right)\left( {1 + 2w_{10}^{*} } \right) + 3R^{*} h^{*} \frac{{dw_{10}^{*} }}{{dx^{*} }}} \right)\frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }} \hfill \\ \end{aligned} \right) \\ & \;\;\;\;\;\;\;\;\;\;\; - \frac{{5\varepsilon R^{*} \theta_{2} }}{6}\frac{d}{{dx^{*} }}\left( {R^{*} h^{*} u_{10}^{*} } \right) + R^{*} h^{*} Z_{2} \theta_{1} \left( {w_{10}^{*} + 1} \right){ ; }A_{0,41} = - \varepsilon^{2} \left( {\frac{{Z_{2} h^{*2} }}{12}\left( {\frac{{d^{2} w_{00}^{*} }}{{dx^{*2} }} + \frac{{d^{2} \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*2} }}} \right) + \frac{1}{{12h^{*} }}\frac{d}{{dx^{*} }}\left( {R^{*} h^{*3} \frac{{dw_{10}^{*} }}{{dx^{*} }}} \right)} \right) + R^{*} \theta_{1} \left( {1 + w_{10}^{*} } \right) \\ & A_{0,42} = \frac{{5\varepsilon h^{*} Z_{2} \theta_{2} }}{24}\frac{{dh^{*} }}{{dx^{*} }}\left( {w_{10}^{*} + 1} \right){ ; }A_{0,43} = Z_{2} \theta_{1} \left( { - \frac{{\varepsilon^{2} }}{{12h^{*} }}\frac{d}{{dx^{*} }}\left( {h^{*3} \frac{{dw_{10}^{*} }}{{dx^{*} }}} \right) + \left( {w_{10}^{*} + 1} \right)} \right) \\ \end{aligned}$$
$$\begin{aligned} A_{0,44} = & - \varepsilon^{2} \left( \begin{aligned} \frac{{h^{*2} Z_{2} \theta_{1} }}{12}\frac{{d^{2} w_{00}^{*} }}{{dx^{*2} }}(2 + w_{10}^{*} ) + \frac{{h^{*2} Z_{2} (5\theta_{2} + 6\theta_{1} )}}{72}\frac{{dw_{10}^{*} }}{{dx^{*} }}\frac{{dw_{00}^{*} }}{{dx^{*} }} + \frac{{R^{*} h^{*2} (5\theta_{2} + 3\theta_{1} )}}{72}\left( {\frac{{dw_{10}^{*} }}{{dx^{*} }}} \right)^{2} + \frac{{R^{*} \theta_{1} }}{2}\left( {\frac{{dw_{00}^{*} }}{{dx^{*} }}} \right)^{2} + \frac{{5h^{*} Z_{2} \theta_{2} }}{12}\frac{{dh^{*} }}{{dx^{*} }}\frac{{dw_{00}^{*} }}{{dx^{*} }} \hfill \\ + \left( {w_{10}^{*} + 1} \right)\left( {(5\theta_{2} + 3\theta_{1} )\left( {\frac{{h^{*2} }}{36}\frac{{dR^{*} }}{{dx^{*} }} + \frac{{R^{*} h^{*} }}{12}\frac{{dh^{*} }}{{dx^{*} }}\frac{{dw_{10}^{*} }}{{dx^{*} }} + \frac{{R^{*} h^{*2} }}{12}} \right)\frac{{d^{2} w_{10}^{*} }}{{dx^{*2} }} + \frac{{5h^{*2} Z_{2} \theta_{2} }}{36}\frac{{d^{2} w_{00}^{*} }}{{dx^{*2} }}} \right) + \frac{{5R^{*} h^{*} \theta_{2} }}{6}\left( {1 + 2w_{10}^{*} } \right)\frac{{d^{2} \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*2} }} \hfill \\ + \frac{{h^{*3} Z_{2} }}{720}\left( {(60\theta_{1} + 100\theta_{2} )w_{10}^{*} + (120\theta_{1} + 50\theta_{2} )} \right)\frac{{d^{2} \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*2} }} + \frac{{h^{*} Z_{2} }}{360}\left( {h^{*2} \frac{{dw_{10}^{*} }}{{dx^{*} }}\left( {30\theta_{1} + 25\theta_{2} } \right)} \right) + h^{*} \frac{{dh^{*} }}{{dx^{*} }}\theta_{2} \left( {150w_{10}^{*} + 75} \right) - \frac{{360R^{*} \theta_{1} }}{{Z_{2} }}\frac{{dw_{00}^{*} }}{{dx^{*} }})\frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }} \hfill \\ \end{aligned} \right) \\ & + \varepsilon \left( { - \frac{{5h^{*} Z_{2} \theta_{2} }}{24}\frac{{dh^{*} }}{{dx^{*} }}u_{10}^{*} + \frac{{h^{*2} Z_{2} (5\theta_{2} + 6\theta_{1} )}}{72}\frac{{du_{10}^{*} }}{{dx^{*} }}} \right) + Z_{2} \theta_{1} w_{00}^{*} + \frac{3}{2}R^{*} w_{10}^{*} \left( {w_{10}^{*} + 2} \right) + R^{*} + R^{*} \theta_{1} V_{00}^{*} \\ \end{aligned}$$
$$\begin{aligned} & \, A_{1,12} = \frac{{\varepsilon h^{*3} Z_{2} }}{12}{ ; }A_{1,13} = \frac{{\varepsilon^{2} h^{*3} Z_{2} }}{12}\frac{{dw_{10}^{*} }}{{dx^{*} }} + \varepsilon^{2} R^{*} h^{*} \left( {\frac{{dw_{00}^{*} }}{{dx^{*} }}{ + }\frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }}} \right){ + ; }A_{1,14} = \frac{{\varepsilon^{2} h^{*3} }}{12}\left( {R^{*} \frac{{dw_{10}^{*} }}{{dx^{*} }} + Z_{2} \left( {\frac{{dw_{00}^{*} }}{{dx^{*} }} + \frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }}} \right)} \right){ ; }A_{1,21} = \frac{{\varepsilon h^{*2} Z_{2} }}{12} \, \\ & A_{1,22} = \frac{{\varepsilon^{2} h^{*2} }}{12}\left( {\frac{{dR^{*} }}{{dx^{*} }} + \frac{{3R^{*} }}{{h^{*} }}\frac{{dh^{*} }}{{dx^{*} }}} \right){ ; }A_{1,23} = \frac{{\varepsilon^{3} h^{*2} }}{12}\left( {R^{*} \frac{{d^{2} w_{10}^{*} }}{{dx^{*2} }} + \frac{{Z_{2} }}{{h^{*3} }}\frac{d}{{dx^{*} }}\left( {h^{*3} \frac{{dw_{00}^{*} }}{{dx^{*} }}} \right) + \frac{1}{{h^{*3} }}\frac{d}{{dx^{*} }}(R^{*} h^{*3} )\frac{{dw_{10}^{*} }}{{dx^{*} }} - \frac{{10R^{*} \theta_{2} }}{{\varepsilon^{2} h^{*2} }}(w_{10}^{*} + 1) + h^{*} Z_{2} \frac{{d^{2} \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*2} }} + 3Z_{2} \frac{{dh^{*} }}{{dx^{*} }}\frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }}} \right) \\ & A_{1,24} = \frac{{\varepsilon^{3} h^{*2} }}{12}\left( {R^{*} \left( {\frac{{d^{2} w_{00}^{*} }}{{dx^{*2} }} + \frac{{d^{2} \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*2} }}} \right) + \frac{{3Z_{2} }}{{20h^{*3} }}\frac{d}{{dx^{*} }}\left( {h^{*5} \frac{{dw_{10}^{*} }}{{dx^{*} }}} \right) + \frac{1}{{h^{*3} }}\frac{d}{{dx^{*} }}\left( {R^{*} h^{*3} } \right)\frac{{dw_{00}^{*} }}{{dx^{*} }} + \left( {3R^{*} \frac{{dh^{*} }}{{dx^{*} }} + \frac{{dR^{*} }}{{dx^{*} }}} \right)\frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }}} \right) + \frac{{h^{*2} \varepsilon }}{12}\left( {Z_{2} \theta_{1} \left( {2 + w_{10}^{*} } \right) - \frac{{5Z_{2} \theta_{2} }}{6}\left( {w_{10}^{*} + 1} \right)} \right) \, \\ & A_{1,32} = - \frac{{\varepsilon^{3} R^{*2} h^{*3} }}{12}\frac{{d^{2} w_{10}^{*} }}{{dx^{*2} }} - \frac{{5\varepsilon R^{*2} h^{*} \theta_{2} }}{6}(w_{10}^{*} + 1) \, \\ & A_{1,33} = - \frac{{\varepsilon^{4} R^{*} h^{*3} }}{12}\left( {\left( {R^{*} \frac{{dw_{10}^{*} }}{{dx^{*} }} + \frac{{Z_{2} }}{2}\frac{{dw_{00}^{*} }}{{dx^{*} }} + Z_{2} \frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }}} \right)\frac{{d^{2} w_{10}^{*} }}{{dx^{*2} }}} \right) - \frac{{\varepsilon^{2} R^{*} h^{*3} }}{12}\left( { - \frac{{12Z_{2} \theta_{1} }}{{h^{*2} }}\left( {\frac{{dw_{00}^{*} }}{{dx^{*} }} + \frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }}} \right) + \frac{{10\theta_{2} }}{{h^{*3} }}\frac{d}{{dx^{*} }}\left( {R^{*} h^{*} } \right)\left( {1 + w_{10}^{*} } \right)^{2} + \frac{{30R^{*} \theta_{2} }}{{h^{*2} }}\left( {\frac{{dw_{10}^{*} }}{{dx^{*} }}(1 + w_{10}^{*} } \right))} \right) \\ & A_{1,34} = - \frac{{R^{*} h^{*3} }}{12}\left( {\varepsilon^{4} \left( {R^{*} + \frac{{3Z_{2} h^{*2} }}{20}\frac{{dw_{10}^{*} }}{{dx^{*} }} + \frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }}} \right)\left( {\frac{{d^{2} w_{10}^{*} }}{{dx^{*2} }}} \right) + \varepsilon^{2} \left( \begin{aligned} - \frac{{30R^{*} \theta_{2} }}{{h^{*2} }}\frac{{dw_{00}^{*} }}{{dx^{*} }}\left( {1 + w_{10}^{*} } \right) - \frac{{5Z_{2} \theta_{2} }}{{2h^{*} }}\frac{{dh^{*} }}{{dx^{*} }}\left( {1 + w_{10}^{*} } \right)^{2} \hfill \\ + Z_{2} \left( {\theta_{1} - \frac{{5\theta_{2} }}{2}\left( {w_{10}^{*} + 2} \right)} \right)\frac{{dw_{10}^{*} }}{{dx^{*} }} - \frac{{5R^{*} h^{*} \theta_{2} }}{6}\left( {3w_{10}^{*} + 1} \right)\frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }} \hfill \\ \end{aligned} \right)} \right) + \frac{{5\varepsilon R^{*2} h^{*} \theta_{2} }}{3}u_{10}^{*} \, \\ & A_{1,41} = - \frac{{\varepsilon^{2} R^{*} h^{*2} }}{12}\frac{{dw_{10}^{*} }}{{dx^{*} }}{ ; }A_{1,42} = - \varepsilon^{3} \left( {\frac{{R^{*} h^{*2} }}{12}\frac{{d^{2} w_{00}^{*} }}{{dx^{*2} }} + \frac{{Z_{2} }}{{80h^{*} }}\frac{d}{{dx^{*} }}\left( {h^{*5} \frac{{dw_{10}^{*} }}{{dx^{*} }}} \right)} \right) - \varepsilon h^{*2} Z_{2} \left( {\frac{{\theta_{1} }}{12}\left( {w_{10}^{*} + 2} \right) + \frac{{5\theta_{2} }}{72}\left( {1 + w_{10}^{*} } \right)} \right) \\ \end{aligned}$$
$$A_{1,43} = - \varepsilon^{4} \left( \begin{aligned} \frac{{R^{*} h^{*} }}{6}\frac{{dw_{10}^{*} }}{{dx^{*} }}\left( {h^{*} \frac{{d^{2} w_{00}^{*} }}{{dx^{*2} }} + \frac{3}{2}\frac{{dw_{00}^{*} }}{{dx^{*} }}} \right) + \frac{{d^{2} w_{10}^{*} }}{{dx^{*2} }}\left( {\frac{{Z_{2} h^{*4} }}{40}\frac{{dw_{10}^{*} }}{{dx^{*} }} + \frac{{R^{*} h^{*2} }}{12}\frac{{dw_{00}^{*} }}{{dx^{*} }}} \right) + \frac{{h^{*3} Z_{2} }}{16}\frac{{dh^{*} }}{{dx^{*} }}\left( {\frac{{dw_{10}^{*} }}{{dx^{*} }}} \right)^{2} + 360R^{*} \theta_{1} w_{10}^{*} + 1)\frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }} \hfill \\ + \frac{{h^{*2} }}{12}\left( {\frac{{dR^{*} }}{{dx^{*} }}\frac{{dw_{10}^{*} }}{{dx^{*} }} + Z_{2} \frac{{d^{2} w_{00}^{*} }}{{dx^{*2} }}} \right)\frac{{dw_{00}^{*} }}{{dx^{*} }} + \frac{1}{{\varepsilon^{2} }}\left( {\frac{{5h^{*} Z_{2} \theta_{2} }}{24}\frac{{dh^{*} }}{{dx^{*} }}\left( {1 + w_{10}^{*} } \right)^{2} + \left( {w_{10}^{*} + 1} \right)\left( {h^{*2} Z_{2} \frac{{dw_{10}^{*} }}{{dx^{*} }}\left( {\frac{{5\theta_{2} }}{72} + \frac{{\theta_{1} }}{12}} \right) + R^{*} \theta_{1} \frac{{dw_{00}^{*} }}{{dx^{*} }}} \right)} \right) \hfill \\ + \frac{{h^{*2} }}{12}\left( {2R^{*} \frac{{dw_{10}^{*} }}{{dx^{*} }} + Z_{2} \left( {\frac{{dw_{00}^{*} }}{{dx^{*} }} + \frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }}} \right)} \right)\frac{{d^{2} \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*2} }} + \frac{{h^{*} }}{360}\left( {30h^{*2} \left( {R^{*} \frac{{d^{2} w_{10}^{*} }}{{dx^{*2} }} + Z_{2} \frac{{d^{2} w_{00}^{*} }}{{dx^{*2} }}} \right)} \right) + \frac{{dw_{10}^{*} }}{{dx^{*} }}\left( {90R^{*} h^{*} \frac{{dh^{*} }}{{dx^{*} }} + 30h^{*2} \frac{{dR^{*} }}{{dx^{*} }}} \right) \hfill \\ \end{aligned} \right)$$
$$\begin{aligned} A_{1,44} = & - \varepsilon^{4} \left( \begin{aligned} \left( {\frac{{R^{*} h^{*2} }}{6}\frac{{dw_{00}^{*} }}{{dx^{*} }} + \frac{{3h^{*4} Z_{2} }}{80}\frac{{dw_{10}^{*} }}{{dx^{*} }}} \right)\frac{{d^{2} w_{00}^{*} }}{{dx^{*2} }} + \left( {\frac{{h^{*4} Z_{2} }}{40}\frac{{dw_{00}^{*} }}{{dx^{*} }} + \frac{{3R^{*} h^{*4} }}{80}\frac{{dw_{10}^{*} }}{{dx^{*} }}} \right)\frac{{d^{2} w_{10}^{*} }}{{dx^{*2} }} + \left( {9h^{*4} Z_{2} \frac{{d^{2} w_{10}^{*} }}{{dx^{*2} }}} \right)\frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }} \hfill \\ + \frac{{h^{*3} Z_{2} }}{8}\frac{{dh^{*} }}{{dx^{*} }}\frac{{dw_{10}^{*} }}{{dx^{*} }}\frac{{dw_{00}^{*} }}{{dx^{*} }} + \left( {\frac{{h^{*2} }}{24}\frac{{dR^{*} }}{{dx^{*} }} + \frac{{R^{*} h^{*} }}{8}\frac{{dh^{*} }}{{dx^{*} }}} \right)\left( {\frac{{dw_{00}^{*} }}{{dx^{*} }}} \right)^{2} + \left( {\frac{{3R^{*} h^{*3} }}{32}\frac{{dh^{*} }}{{dx^{*} }} + \frac{{3h^{*4} }}{160}\frac{{dR^{*} }}{{dx^{*} }}} \right)\left( {\frac{{dw_{10}^{*} }}{{dx^{*} }}} \right)^{2} \hfill \\ + \frac{{h^{*3} }}{720}\left( {27h^{*2} Z_{2} \frac{{dw_{10}^{*} }}{{dx^{*} }} + 120R^{*} \frac{{dw_{00}^{*} }}{{dx^{*} }} + 60R^{*} \frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }}} \right)\frac{{d^{2} \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*2} }} + \frac{{h^{*} }}{360}(45h^{*3} Z_{2} \frac{{dh^{*} }}{{dx^{*} }}\frac{{dw_{10}^{*} }}{{dx^{*} }} + 30h^{*2} \frac{{dR^{*} }}{{dx^{*} }}\frac{{dw_{00}^{*} }}{{dx^{*} }} \hfill \\ + 60R^{*} h^{*2} \frac{{d^{2} w_{00}^{*} }}{{dx^{*2} }} + 90R^{*} h^{*} \frac{{dh^{*} }}{{dx^{*} }}\frac{{dw_{00}^{*} }}{{dx^{*} }} + \frac{1}{\varepsilon }\left( {\frac{{h^{*3} Z_{2} }}{16}\frac{{dh^{*} }}{{dx^{*} }}\frac{{du_{10}^{*} }}{{dx^{*} }} + \frac{{h^{*4} Z_{2} }}{80}\frac{{d^{2} u_{10}^{*} }}{{dx^{*2} }}} \right) \hfill \\ \end{aligned} \right) \\ & - \varepsilon^{2} \left( \begin{aligned} \left( {\frac{{h^{*2} \theta_{1} }}{24}\frac{{dR^{*} }}{{dx^{*} }} + \frac{{R^{*} h^{*} \theta_{1} }}{8}\frac{{dh^{*} }}{{dx^{*} }}} \right)\left( {w_{10}^{*2} + 2w_{10}^{*} } \right) + \left( {\frac{{5h^{*2} \theta_{2} }}{72}\frac{{dR^{*} }}{{dx^{*} }} + \frac{{5R^{*} h^{*} \theta_{2} }}{24}\frac{{dh^{*} }}{{dx^{*} }}} \right)\left( {1 + w_{10}^{*} } \right)^{2} + \left( {\frac{{R^{*} }}{4}\frac{{dh^{*} }}{{dx^{*} }} + \frac{{h^{*} }}{12}\frac{{dR^{*} }}{{dx^{*} }}} \right)h^{*} V_{00}^{*} + \hfill \\ \frac{{R^{*} h^{*2} }}{12}\frac{{dV_{00}^{*} }}{{dx^{*} }} + \frac{{dh^{*} }}{{dx^{*} }}\frac{{h^{*} Z_{2} \theta_{1} }}{4}w_{00}^{*} + \left( {\frac{{5^{*2} Z_{2} (5\theta_{2} + 6\theta_{1} )}}{72}\frac{{dw_{00}^{*} }}{{dx^{*} }} + \frac{{R^{*} h^{*2} (5\theta_{2} + 3\theta_{1} )}}{36}\frac{{dw_{10}^{*} }}{{dx^{*} }}} \right)\left( {1 + w_{10}^{*} } \right) \hfill \\ + h^{*2} Z_{2} \left( {(25\theta_{2} - 30\theta_{1} )w_{10}^{*} + (25\theta_{2} - 60\theta_{1} )} \right)\frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }} \hfill \\ \end{aligned} \right) \\ \end{aligned}$$
$$\begin{aligned} & A_{2,22} = \frac{{\varepsilon^{2} R^{*} h^{*2} }}{12} \, ; \, A_{2,23} = \frac{{\varepsilon^{3} h^{*2} }}{12}\left( {R^{*} \frac{{dw_{10}^{*} }}{{dx^{*} }} + Z_{2} \left( {\frac{{dw_{00}^{*} }}{{dx^{*} }} + \frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }}} \right)} \right) \, ; \, A_{2,24} = \frac{{\varepsilon^{3} h^{*2} }}{12}\left( {R^{*} \left( {\frac{{dw_{00}^{*} }}{{dx^{*} }} + \frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }}} \right) + \frac{{3h^{*2} Z_{2} }}{20}\frac{{dw_{10}^{*} }}{{dx^{*} }}} \right) \, ;A_{2,33} = \varepsilon^{3} R^{*} P_{1}^{*} - \frac{{10\varepsilon^{2} R^{*2} h^{*} \theta_{2} }}{12}\left( {1 + w_{10}^{*} } \right)^{2} \\ & A_{2,34} = \frac{{\varepsilon^{4} R^{*} h^{*3} }}{12}\left( {R^{*} \left( {\frac{{dw_{00}^{*} }}{{dx^{*} }} - \frac{{3Z_{2} h^{*2} }}{40}\frac{{dw_{10}^{*} }}{{dx^{*} }} - \frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }}} \right)\frac{{dw_{10}^{*} }}{{dx^{*} }} - Z_{2} \frac{{dw_{00}^{*} }}{{dx^{*} }}\frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }} - \frac{{Z_{2} }}{2}\left( {\frac{{dw_{00}^{*} }}{{dx^{*} }}} \right)^{2} } \right) - \frac{{\varepsilon^{3} R^{*2} h^{*3} }}{12}\frac{{du_{10}^{*} }}{{dx^{*} }} - \frac{{\varepsilon^{2} R^{*} h^{*3} }}{12}\left( {V_{00}^{*} + \frac{{5Z_{2} \theta_{2} }}{6}\left( {1 + w_{10}^{*} } \right)^{2} + \frac{{Z_{2} \theta_{1} }}{2}w_{10}^{*} \left( {w_{10}^{*} + 4} \right)} \right)\,\,\, \\ & \, A_{2,42} = \frac{{\varepsilon^{3} h^{*4} Z_{2} }}{80}\frac{{dw_{10}^{*} }}{{dx^{*} }} \, ; \, A_{2,43} = - \varepsilon^{4} \left( \begin{aligned} \frac{{R^{*} h^{*2} }}{6}\left( {\frac{{dw_{00}^{*} }}{{dx^{*} }}\frac{{dw_{10}^{*} }}{{dx^{*} }}} \right) + \frac{3}{160}h^{*4} Z_{2} \left( {\frac{{dw_{10}^{*} }}{{dx^{*} }}} \right)^{2} \hfill \\ + \frac{{h^{*2} Z_{2} }}{24}\left( {\frac{{dw_{00}^{*} }}{{dx^{*} }}} \right)^{2} + \frac{{h^{*3} }}{12}\left( {2R^{*} \frac{{dw_{10}^{*} }}{{dx^{*} }} + Z_{2} \frac{{dw_{00}^{*} }}{{dx^{*} }}} \right)\frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }} \hfill \\ \end{aligned} \right) - \varepsilon^{3} \left( {\frac{{R^{*} h^{*2} }}{12}\frac{{du_{10}^{*} }}{{dx^{*} }}} \right) - \varepsilon^{2} h^{*2} Z_{2} \left( {\frac{1}{12}V_{00}^{*} + \frac{{5\theta_{2} }}{72}\left( {w_{10}^{*} + 1} \right)^{2} + \frac{{\theta_{1} w_{10}^{*} }}{24}\left( {w_{10}^{*} + 4} \right)} \right) \, \\ & A_{2,44} = - \varepsilon^{4} h^{*2} \left( \begin{aligned} \frac{{R^{*} }}{24}\left( {\frac{{dw_{00}^{*} }}{{dx^{*} }}} \right)^{2} + \frac{{h^{*2} Z_{2} }}{40}\frac{{dw_{00}^{*} }}{{dx^{*} }}\frac{{dw_{10}^{*} }}{{dx^{*} }} + \frac{{3R^{*} h^{*2} }}{160}\left( {\frac{{dw_{10}^{*} }}{{dx^{*} }}} \right)^{2} \hfill \\ + \frac{{h^{*} }}{360}\left( {9Z_{2} \frac{{dw_{10}^{*} }}{{dx^{*} }} + 30R^{*} \frac{{dw_{00}^{*} }}{{dx^{*} }}} \right)\frac{{d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w}^{*} }}{{dx^{*} }} \hfill \\ \end{aligned} \right) - \varepsilon^{3} \left( {\frac{{h^{*4} Z_{2} }}{80}\frac{{du_{10}^{*} }}{{dx^{*} }}} \right) - \varepsilon^{2} R^{*} h^{*2} \left( {\frac{{5\theta_{2} }}{72}\left( {w_{10}^{*} + 1} \right)^{2} + \frac{{\theta_{1} w_{10}^{*} }}{24}\left( {w_{10}^{*} + 2} \right) + \frac{1}{12}V_{00}^{*} + \frac{{Z_{2} \theta_{1} }}{{12R^{*} }}w_{00}^{*} } \right) \\ \end{aligned}$$
