how to find the solution of the ode y”-2y’+8y=e^xSolution : Given non homogeneous linear ode y”-2y’+8y=e^x \[y^{\prime\prime}-2y^\prime+8y=e^x\] Subject to initial conditions \[ y\left(0\right)=1,\ y^\prime\left(0\right)=-1 \] \[\frac{d^2y}{dx^2}-2\frac{dy}{dx}+8y=e^x\] Let D=d/dx \[D^2y-2Dy+8y=e^x\] \[\left(D^2-2D+8\right)y=e^x\] Step 1: To find complementary solution (yc) that is to…
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