Pregunta: Demuestre que: y(x) = 20 cos (5 lnx) X 3 sen (slnx) X Es una Solución a la ED: 3 x³y + 2x²y" + 20xy²-78y=0 X

The given differential equation is

${\mathrm{x}}^3\mathrm{y}{}^{‴}+2{\mathrm{x}}^2\mathrm{y}{}^{″}+20\mathrm{x}{\mathrm{y}}^{\prime }-78\mathrm{y}=0$ ..........(1)

Now here to show that $\mathrm{y}\left(\mathrm{x}\right)=\frac{20\cos \left(5\ln \mathrm{x}\right)}{\mathrm{x}}-\frac{3\sin \left(5\ln \mathrm{x}\right)}{\mathrm{x}}$ is a solution of (1...