Question $9$

$5$ pts

Find the general solution to the given linear differential equation.

$\frac{dy}{dx}\frac{y}{x}=x^3{e}^x$

$y=\frac{c}{x}{x}^3{e}^x-4x^2{e}^{x}12x{e}^x-24e^{x}48e^x$

$y=\frac{c}{x}{x}^3{e}^x-4x^2{e}^{x}12x{e}^x-12e^{x}24\frac{e^x}{x}$

$y=\frac{c}{x}{x}^3{e}^x-4x^2{e}^{x}12x{e}^x-24e^{x}24e^x$

$y=\frac{c}{x}{x}^3{e}^x-4x^2{e}^{x}12x{e}^x-24e^{x}24\frac{e^x}{x}$

$y=\frac{c}{x}{x}^3{e}^x-4x^2{e}^{x}12x{e}^x-24e^{x}48\frac{e^x}{x}$