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

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

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

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

y = - ln (- \frac{1}{3} (x^{2} + 1)^{\frac{3}{2}} - c_{1})

Solution steps

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

Solve separable ODE:

y = - ln (- \frac{1}{3} (x^{2} + 1)^{\frac{3}{2}} - c_{1})

y = - ln (- \frac{1}{3} (x^{2} + 1)^{\frac{3}{2}} - c_{1})

\int \frac{4}{x ^{2} - 1} d x

\frac{d}{d x} (- \frac{1}{2} sin (x))

\int \frac{x ^{2}}{a ^{2} - x ^{2}} d x

e^{x}, e^{- x}, [- 1, 1]

\int \frac{1}{( x ^{2} - 121 ) ^{\frac{3}{2}}} d x

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