What is the solution for y^'= t/(1+t^2)*e^y ?

The solution for y^'= t/(1+t^2)*e^y is y=-ln(-1/2 ln(1+t^2)-c_{1})

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y^'= t/(1+t^2)*e^y

y^{^{'}} = \frac{t}{1 + t ^{2}} \cdot e^{y}

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

Solution steps

y^{'} (t) = \frac{t}{1 + t ^{2}} \cdot e^{y}

Solve separable ODE:

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

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

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What is the solution for y^'= t/(1+t^2)*e^y ?
The solution for y^'= t/(1+t^2)*e^y is y=-ln(-1/2 ln(1+t^2)-c_{1})