What is the solution for e^y(1+x^2)dy-2x(1+e^y)dx=0 ?

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

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e^y(1+x^2)dy-2x(1+e^y)dx=0

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

y = ln (e^{c_{1}} + e^{c_{1}} x^{2} - 1)

Solution steps

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

Solve separable ODE:

y = ln (e^{c_{1}} + e^{c_{1}} x^{2} - 1)

y = ln (e^{c_{1}} + e^{c_{1}} x^{2} - 1)

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