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

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

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(1+x^2)((dy)/(dx))+xe^{-y}=0

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

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

Solution steps

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

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})

y - 2 x y^{^{'}} = 0

x^{2} (y^{^{'}})^{1} - 3 x y^{^{'}} + 16 y = 0

\frac{d y}{d x} = 100 - \frac{y}{100}

\frac{d y}{d x} = \frac{( y ^{2} )}{x}, y (1) = \frac{1}{3}

y^{'} (t) = y (y + 1)^{2}, y (0) = 1.2

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