Solved: Consider the differential equation where a, b, and

Chapter , Problem 14RP

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Consider the differential equation \(a y^{\prime \prime}+b y^{\prime}+c y=g(x)\) where a, b, and c are constants. Choose the input functions g(x) for which the method of undetermined coefficients is applicable and the input functions for which the method of variation of parameters is applicable.

(a) \(g(x)=e^{x} \ln x\)

(b) \(g(x)=x^{3} \cos x\)

(c) \(g(x)=\frac{\sin x}{e^{x}}\)

(d) \(g(x)=2 x^{-2} e^{x}\)

(e) \(g(x)=\sin ^{2} x\)

(f) g(x)=\frac{e^{x}}{\sin x}

Text Transcription:

ay^prime\prime+b y^prime+c y=g(x)

g(x)=e^xlnx

g(x)=x^3cosx

g(x)=fracsinxe^x

g(x)=2 x^-2e^x

g(x)=\sin^2x

g(x)=\frace^xsinx