What is a solution to the differential equation dydx=xey?

y′=xeye−yy′=x∫e−yy′dx=∫xdx∫e−ydy=∫xdx−e−y=x22+Ce−y=C−x22−y=ln⁡(C−x22)y=−ln⁡(C−x22)y=ln⁡(1C−x22)

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delitzo1d4

2022-04-18

What is a solution to the differential equation

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

fallendreamsit2p

Beginner2022-04-19Added 14 answers

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

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

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

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

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

e^{- y} = C - \frac{x^{2}}{2}

- y = \ln (C - \frac{x^{2}}{2})

y = - \ln (C - \frac{x^{2}}{2})

y = \ln (\frac{1}{C - \frac{x^{2}}{2}})

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