What is the solution for (y^')/(1+y^2)+t/(e^{t^2)}=0,y(0)=1 ?

The solution for (y^')/(1+y^2)+t/(e^{t^2)}=0,y(0)=1 is y=tan(1/2 e^{-t^2}+pi/4-1/2)

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

\frac{y ^{^{'}}}{1 + y ^{2}} + \frac{t}{e ^{t^{2}}} = 0, y (0) = 1

y = tan (\frac{1}{2} e^{- t^{2}} + \frac{π}{4} - \frac{1}{2})

Solution steps

\frac{y ^{'} ( t )}{1 + y ^{2}} + \frac{t}{e ^{t^{2}}} = 0

Solve separable ODE:

y = tan (\frac{1}{2} e^{- t^{2}} + \frac{π}{4} - \frac{1}{2})

y = tan (\frac{1}{2} e^{- t^{2}} + \frac{π}{4} - \frac{1}{2})

\frac{d}{d x} (\frac{11}{x})

\int 2 x (x^{2} - 7)^{6} d x

\int_{\frac{1}{7}}^{3} 12 x ln (7 x) d x

\frac{d}{d x} (\frac{sin ( x )}{x ^{3}})

What is the solution for (y^')/(1+y^2)+t/(e^{t^2)}=0,y(0)=1 ?
The solution for (y^')/(1+y^2)+t/(e^{t^2)}=0,y(0)=1 is y=tan(1/2 e^{-t^2}+pi/4-1/2)