Solve the differential equation yeyxdx=(xeyx+y2)dy(y=0)

Solution: as, dxdy=xeyx+y2yeyx dydx=yx+eyxy yeyxdydx=xeyx+y2 eyx(y.dydx−x)=y2 let yx=t y2dydx⋅y−x=dt et⋅(dydt)=1 ∫etdt=∫dt et=y+c eyx=y+c answer

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Solve the differential equation {y}{e}^{{{{x}}{{y}}}}{.{d}{x}.

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Solve the differential equation $y e^{\frac{x}{y}} d x = (x e^{\frac{x}{y}} + y^{2}) d y (y \neq = 0)$

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Solve the differential equation

y e^{\frac{x}{y}} d x = (x e^{\frac{x}{y}} + y^{2}) d y (y \neq = 0)

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Solution: as,

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

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

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

e^{\frac{x}{y}} (y . \frac{d x}{d y} - x) = y^{2}

let

\frac{x}{y} = t

\frac{\frac{d x}{d y} \cdot y - x}{y ^{2}} = d t

e^{t} \cdot (\frac{d t}{d y}) = 1

\int e^{t} d t = \int d t

e^{t} = y + c

e^{\frac{x}{y}} = y + c

answer

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Question Text	Solve the differential equation $y e^{\frac{x}{y}} d x = (x e^{\frac{x}{y}} + y^{2}) d y (y \neq = 0)$
Answer Type	Text solution:1
Upvotes	150