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

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

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

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

y = \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x}) + c_{1}

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = x e^{- 2 x}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int x e^{- 2 x} d x

\int x e^{- 2 x} d x = \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x}) + c_{1}

y = \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x}) + c_{1}

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