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

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

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(dy)/(dx)=4xe^{2x}

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

y = 2 e^{2 x} x - e^{2 x} + c_{1}

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 4 x e^{2 x}

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

then

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

y = \int 4 x e^{2 x} d x

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

y = 2 e^{2 x} x - e^{2 x} + c_{1}

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