What is the solution for ((1-x^2)dy)/(dx)=xe^y ?

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

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((1-x^2)dy)/(dx)=xe^y

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

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

Solution steps

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

Solve separable ODE:

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

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

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