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

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

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

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

y = ln (e^{2 a r c t a n (x) + c_{1}} - 1)

Solution steps

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

Solve separable ODE:

y = ln (e^{2 a r c t a n (x) + c_{1}} - 1)

y = ln (e^{2 a r c t a n (x) + c_{1}} - 1)

\frac{d y}{d x} = e^{x} y^{3}

y^{^{'}} = (5 x + 1) (y + 11), y (0) = 0

x^{2} sin (x d x) + x y d y = 0

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

sinh (x) d x + y^{- 1} cosh (x) d y = 0

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