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Question Number 65219 by Rio Michael last updated on 26/Jul/19

Commented by Rio Michael last updated on 26/Jul/19

$$pleasecheckmysolutionandcorrectmeforthatquestion$$$$youcangivenewmethodstosolveplease.$$

Answered by Tanmay chaudhury last updated on 26/Jul/19

$$2\frac{d^{2}y}{{dx}^2}-\frac{dy}{dx}-3y=5e^{-x}$$$$lety=e^{mx}$$$$complimentaryfunction$$$$2m^2-m-3=0$$$$2m^2-3m+2m-3=0$$$$m(2m-3)+1(2m-3)=0$$$$(2m-3)(m+1)=0$$$$$$$$so\mathit{C}.\mathit{F}=C_1{e}^{\frac{3x}{2}}+C_2{e}^{-x}$$$$P.I$$$$y_{\mathit{p}.\mathit{i}}=\frac{5e^{-x}}{2D^2-D-3}[Dy=\frac{dy}{dx}and{D}^{2}y=\frac{d^{2}y}{{dx}^2}]$$$$y_{\mathit{p}.\mathit{I}}=\frac{5e^{-x}}{(D+1)(2D-3)}$$$$y_{p.I}=\frac{5e^{-x}}{2(-1)-3}\times \frac{1}{D-1+1}$$$$y_{p.I}=\frac{5e^{-x}}{-5}\times x$$$$=-{xe}^{-x}$$$$\mathit{c}\mathit{o}\mathit{m}\mathit{p}\mathit{l}\mathit{e}\mathit{t}\mathit{e}\mathit{a}\mathit{n}\mathit{s}\mathit{w}\mathit{e}\mathit{r}$$$$\mathit{y}=C_1{e}^{\frac{3x}{2}}+C_2{e}^{-x}-{xe}^{-x}$$$$\mathit{y}\mathit{o}\mathit{u}\mathit{r}\mathit{a}\mathit{n}\mathit{s}\mathit{w}\mathit{e}\mathit{r}\mathit{i}\mathit{s}\mathit{c}\mathit{o}\mathit{r}\mathit{r}\mathit{e}\mathit{c}\mathit{t}$$

Commented by Rio Michael last updated on 26/Jul/19

$$thankyou$$

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