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

The solution for (dy)/(dx)+y=xye^{-4x} is y=e^{1/16 (-4e^{-4x}x-e^{-4x})-x+c_{1}}

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

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

y = e^{\frac{1}{16} (- 4 e^{- 4 x} x - e^{- 4 x}) - x + c_{1}}

Solution steps

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

Solve separable ODE:

y = e^{\frac{1}{16} (- 4 e^{- 4 x} x - e^{- 4 x}) - x + c_{1}}

y = e^{\frac{1}{16} (- 4 e^{- 4 x} x - e^{- 4 x}) - x + c_{1}}

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What is the solution for (dy)/(dx)+y=xye^{-4x} ?
The solution for (dy)/(dx)+y=xye^{-4x} is y=e^{1/16 (-4e^{-4x}x-e^{-4x})-x+c_{1}}