What is the solution for (dy)/(dx)=x^2e^{-4x}-4y ?

The solution for (dy)/(dx)=x^2e^{-4x}-4y is y=(x^3)/(3e^{4x)}+(c_{1})/(e^{4x)}

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(dy)/(dx)=x^2e^{-4x}-4y

\frac{d y}{d x} = x^{2} e^{- 4 x} - 4 y

y = \frac{x ^{3}}{3 e ^{4 x}} + \frac{c _{1}}{e ^{4 x}}

Solution steps

\frac{d y}{d x} = x^{2} e^{- 4 x} - 4 y

Solve linear ODE:

y = \frac{x ^{3}}{3 e ^{4 x}} + \frac{c _{1}}{e ^{4 x}}

y = \frac{x ^{3}}{3 e ^{4 x}} + \frac{c _{1}}{e ^{4 x}}

What is the solution for (dy)/(dx)=x^2e^{-4x}-4y ?
The solution for (dy)/(dx)=x^2e^{-4x}-4y is y=(x^3)/(3e^{4x)}+(c_{1})/(e^{4x)}