In 27–30, is a twoparameter family of the second-order DE

Chapter , Problem 31RP

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In Problems 31–34, \(y=c_{1} e^{3 x}+c_{2} e^{-x}-2 x\) is a two parameter family of the second-order DE \(y^{\prime \prime}-2 y^{\prime}-3 y=6 x+4\). Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions.

y (0) = 0,    \(y^{\prime}(0)=0\)

Text Transcription:

y=c_1 e^3x + c_2 e^-x - 2x

y^prime prime - 2y^prime - 3y = 6x+4

y^prime(0) = 0

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