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

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

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e^x(dy)/(dx)=2x

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

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

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

Isolate

y^{'} (x) : y^{'} (x) = \frac{2 x}{e ^{x}}

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

then

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

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

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

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

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