What is the solution for (dy)/(dx)-(4/x)y=x^5e^x ?

The solution for (dy)/(dx)-(4/x)y=x^5e^x is y=e^xx^5-e^xx^4+c_{1}x^4

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(dy)/(dx)-(4/x)y=x^5e^x

\frac{d y}{d x} - (\frac{4}{x}) y = x^{5} e^{x}

y = e^{x} x^{5} - e^{x} x^{4} + c_{1} x^{4}

Solution steps

\frac{d y}{d x} - (\frac{4}{x}) y = x^{5} e^{x}

Solve linear ODE:

y = e^{x} x^{5} - e^{x} x^{4} + c_{1} x^{4}

y = e^{x} x^{5} - e^{x} x^{4} + c_{1} x^{4}

x \to 2 lim (\frac{x ^{2} - 2}{\frac{5 x}{7} - \frac{5 2}{7}})

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 5)^{5})

\frac{d}{d x} (\frac{x - 5}{x ^{2}})

x \to 6 - lim (c x^{2} + 3 x)

2 y

What is the solution for (dy)/(dx)-(4/x)y=x^5e^x ?
The solution for (dy)/(dx)-(4/x)y=x^5e^x is y=e^xx^5-e^xx^4+c_{1}x^4