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Popular >

e^xy^'=2x

Solution

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

Solution

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

Solution steps

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

Isolate

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

If

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}

Popular Examples

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\int \frac{4}{x ^{2} + 9} d x

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6 x y

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\int_{0}^{\infty} 8 e^{- 4 x} d x

integral from 0 to 5 of 1/4 (5-x)sqrt(x)

\int_{0}^{5} \frac{1}{4} (5 - x) x d x

Frequently Asked Questions (FAQ)

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