Pregunta: Solve y′′ + y = 5xe−3x, y(0) = 0, y′(0) = 0.

Here the given Initial value problem is $\mathrm{y}{}^{″}+\mathrm{y}=5\mathrm{x}{\mathrm{e}}^{-3\mathrm{x}}$ with $\mathrm{y}\left(0\right)=0\text{and}{\mathrm{y}}^{\prime }\left(0\right)=0$

Now, For finding $\mathrm{C}.\mathrm{F}$ let us solve $\mathrm{y}{}^{″}+\mathrm{y}=0$,

The Auxiliary Equation...