What is the solution for (1-x^2)ydy-xe^{-y}dx=0,y(0)=0 ?

The solution for (1-x^2)ydy-xe^{-y}dx=0,y(0)=0 is y=\W((-ln(-(x+1)(x-1))+c_{1})/(2e))+1

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(1-x^2)ydy-xe^{-y}dx=0,y(0)=0

(1 - x^{2}) y d y - x e^{- y} d x = 0, y (0) = 0

y = W (\frac{- ln ( - ( x + 1 ) ( x - 1 ) ) + c _{1}}{2 e}) + 1

Solution steps

(1 - x^{2}) y d y - x e^{- y} d x = 0

Solve separable ODE:

y = W (\frac{- ln ( - ( x + 1 ) ( x - 1 ) ) + c _{1}}{2 e}) + 1

y = W (\frac{- ln ( - ( x + 1 ) ( x - 1 ) ) + c _{1}}{2 e}) + 1

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

(1 + cos (x)) y^{^{'}} = (1 + e^{- y}) sin (x), y (0) = 0

\frac{d y}{d x} = - \frac{0.6}{cos ( y )}

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

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

What is the solution for (1-x^2)ydy-xe^{-y}dx=0,y(0)=0 ?
The solution for (1-x^2)ydy-xe^{-y}dx=0,y(0)=0 is y=\W((-ln(-(x+1)(x-1))+c_{1})/(2e))+1