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First-Order Linear Differential Equations

  • Ravi P. AgarwalEmail author
  • Simona Hodis
  • Donal O’Regan
Chapter
Part of the Problem Books in Mathematics book series (PBM)

Abstract

Consider the first-order linear differential equation \(y'+p(t)y~=~q(t),~~~'=\frac{d~}{dt}\) where the functions p and q are continuous in an open interval \(I=(\alpha ,\beta )\) [1]. We can find the general solution of (1.1) in terms of the known functions p and q by multiplying both sides of (1.1) by an integrating factor \(e^{P(t)}\), where P(t) is a function such that \(P'(t)=p(t)\).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ravi P. Agarwal
    • 1
    Email author
  • Simona Hodis
    • 1
  • Donal O’Regan
    • 2
  1. 1.Department of MathematicsTexas A&M University–KingsvilleKingsvilleUSA
  2. 2.Department of MathematicsNational University of IrelandGalwayIreland

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