What is the solution for e^{x+2y}dx-e^{2x-y}dy=0 ?

The solution for e^{x+2y}dx-e^{2x-y}dy=0 is y=-(ln(3e^{-x}-c_{1}))/3

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e^{x+2y}dx-e^{2x-y}dy=0

e^{x + 2 y} d x - e^{2 x - y} d y = 0

y = - \frac{ln ( 3 e ^{- x} - c _{1} )}{3}

Solution steps

e^{x + 2 y} d x - e^{2 x - y} d y = 0

Solve separable ODE:

y = - \frac{ln ( 3 e ^{- x} - c _{1} )}{3}

y = - \frac{ln ( 3 e ^{- x} - c _{1} )}{3}

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\frac{d}{d x} (x y + 1)

\frac{d}{d x} (3 (sin (2 x) cos (x) - sin^{3} (x)))

What is the solution for e^{x+2y}dx-e^{2x-y}dy=0 ?
The solution for e^{x+2y}dx-e^{2x-y}dy=0 is y=-(ln(3e^{-x}-c_{1}))/3