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Question Number 149274 by BHOOPENDRA last updated on 04/Aug/21

Answered by Olaf_Thorendsen last updated on 05/Aug/21

$$\frac{d^{2}y}{{dx}^2}-3\frac{dy}{dx}+2y=e^x\left(\mathrm{E}\right)$$$$\mathrm{Let}y=e^{x}u,y^{\prime }=e^x(u^{\prime }+u),y^{″}=e^x(u^{″}+2u^{\prime }+u)$$$$\left(\mathrm{E}\right):u^{″}+2u^{\prime }+u-3(u^{\prime }+u)+2u=1$$$$\left(\mathrm{E}\right):u^{″}-u^{\prime }=1$$$$\Rightarrow u^{\prime }=-1,u=a-x$$$$y=e^{x}u=(a-x)e^x$$

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