In 19–22, a particular solution and a fundamental solution

Chapter 6, Problem 19E

(choose chapter or problem)

In Problems 19–22, a particular solution and a fundamental solution set are given for a nonhomogeneous equation and its corresponding homogeneous equation.
(a) Find a general solution to the nonhomogeneous equation. (b) Find the solution that satisfies the specified initial conditions.
                                      \(y^{\prime \prime}+y^{\prime \prime}+3 y-5 y=2+6 x-5 x^{2}\)

                                       \(y(0)=-1, y^{\prime}(0)=1, y^{\prime \prime}(0)=-3 ; y_{p}=x^{2} ;\left\{e^{x}, e^{-x} \cos 2 x, e^{-x} \sin 2 x\right\}\)

Equation Transcription:

Text Transcription:

y'''+y''+3y'-5y=2+6x-5x^2

y(0)=-1, y'(0)=1, y''(0)=-3;y_p=x^2; {e^x,e^-x cos⁡ 2x,e^-x sin ⁡2x}