What is the solution for x(dy)/(dx)+4y=x^{-3}e^x ?

The solution for x(dy)/(dx)+4y=x^{-3}e^x is y=(e^x)/(x^4)+(c_{1})/(x^4)

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x(dy)/(dx)+4y=x^{-3}e^x

x \frac{d y}{d x} + 4 y = x^{- 3} e^{x}

y = \frac{e ^{x}}{x ^{4}} + \frac{c _{1}}{x ^{4}}

Solution steps

x \frac{d y}{d x} + 4 y = x^{- 3} e^{x}

Solve linear ODE:

y = \frac{e ^{x}}{x ^{4}} + \frac{c _{1}}{x ^{4}}

y = \frac{e ^{x}}{x ^{4}} + \frac{c _{1}}{x ^{4}}

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What is the solution for x(dy)/(dx)+4y=x^{-3}e^x ?
The solution for x(dy)/(dx)+4y=x^{-3}e^x is y=(e^x)/(x^4)+(c_{1})/(x^4)