Four Interesting Equations

  • W. Richard Kolk
  • Robert A. Lerman


Four differential equations, (i)–(iv), are presented to show that the consummate uniformity of linear equations is not shared by nonlinear equations
$$\dot x + x = 0$$
$$\dot x + \left| x \right| = 0$$
$$\left| {\dot x} \right| + x = 0$$
$$\left| {\dot x} \right| + \left| x \right| = 0$$
which is illustrated by addressing three essential features of the solutions.


Phase Portrait Interesting Equation Nonlinear System Dynamics Solution Plane Solve Equation 
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References and Related Literature


  1. 1.
    Van Karman, T., and Biot, M., Mathematical Methods in Engineering, McGraw-Hill, New York (1940).Google Scholar
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    Polya, G., How to Solve It, The World of Mathematics, pp. 1980–1992, Simon & Schuster, New York (1956).Google Scholar
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    Gerald, Curtis F. and Wheatley, Patrick O., Applied Numerical Analysis, Addison-Wesley, 3rd edition, Reading, Mass. (1984).Google Scholar

Related Literature

  1. 1.
    Osgood, W. F., Advanced Calculus, Macmillan, New York (1925).MATHGoogle Scholar
  2. 2.
    Spiegel, M., Applied Differential Equations, third edition, Prentice-Hall, Englewood Cliffs, New Jersey (1981).MATHGoogle Scholar
  3. 3.
    Saaty, Thomas L., Modern Nonlinear Equations, Dover, New York (1981).MATHGoogle Scholar
  4. 4.
    Saaty, Thomas L., and Bram, Joseph, Nonlinear Mathematics, Dover, New York (1964).MATHGoogle Scholar
  5. 5.
    Davis, Harold T., Introduction to Nonlinear Differential and Integral Equations, Dover, New York (1962).MATHGoogle Scholar

Copyright information

© Van Nostrand Reinhold 1992

Authors and Affiliations

  • W. Richard Kolk
    • 1
  • Robert A. Lerman
    • 2
  1. 1.PortlandUSA
  2. 2.West HartfordUSA

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