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Popular Calculus >

y^'+xe^{(-x^2)/2}=0

Solution

y^{^{'}} + x e^{\frac{- x ^{2}}{2}} = 0

Solution

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

Solution steps

y^{'} (x) + x e^{\frac{- x ^{2}}{2}} = 0

Isolate

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

If

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

then

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

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

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

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

Graph

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Frequently Asked Questions (FAQ)

What is the solution for y^'+xe^{(-x^2)/2}=0 ?
The solution for y^'+xe^{(-x^2)/2}=0 is y=e^{-(x^2)/2}+c_{1}