Pregunta: Solve the following initial value problem d² dz² y (x) − 7 ( + y (x)) + 10 y (x) = -2 sin (3 z) + 42 cos (3x) with y (0) - 3, y (z) = dy(0) dr - 6

Here the given differential equations is $\frac{{\mathrm{d}}^2}{{\mathrm{d}\mathrm{x}}^2}\mathrm{y}\left(\mathrm{x}\right)-7\left(\frac{\mathrm{d}}{\mathrm{d}\mathrm{x}}\mathrm{y}\left(\mathrm{x}\right)\right)+10\mathrm{y}\left(\mathrm{x}\right)=-2\sin \left(3\mathrm{x}\right)+42\cos \left(3\mathrm{x}\right)$ .....(i)

with $\mathrm{y}\left(0\right)=3,\frac{\mathrm{d}\mathrm{y}\left(0\right)}{\mathrm{d}\mathrm{x}}=6$ .

Let $\mathrm{y}\left(\mathrm{x}\right)={\mathrm{e}}^{\mathrm{m}\mathrm{x}}(\ne 0)$ be the trial solution of the ...