What is the solution for (dy)/(dt)=(2t)/(y+yt^2) ?

The solution for (dy)/(dt)=(2t)/(y+yt^2) is y=sqrt(2ln(1+t^2)+c_{1)},y=-sqrt(2ln(1+t^2)+c_{1)}

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(dy)/(dt)=(2t)/(y+yt^2)

\frac{d y}{d t} = \frac{2 t}{y + y t ^{2}}

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

Solution steps

\frac{d y}{d t} = \frac{2 t}{y + y t ^{2}}

Solve separable ODE:

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

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

y^{^{'}} = x^{3} e^{- y}

y^{^{'}} = 2 x y - 1

y^{^{'}} = y^{2} + 4

\frac{d x}{d t} = r (1 - \frac{x}{k}) x

2 e^{2 x} cos (3 y) d x - 3 e^{2 x} sin (3 y) d y = 0

What is the solution for (dy)/(dt)=(2t)/(y+yt^2) ?
The solution for (dy)/(dt)=(2t)/(y+yt^2) is y=sqrt(2ln(1+t^2)+c_{1)},y=-sqrt(2ln(1+t^2)+c_{1)}