What is the solution for (dy)/(dt)=-2(t+1)y^2,y(0)=-1/8 ?

The solution for (dy)/(dt)=-2(t+1)y^2,y(0)=-1/8 is y=-1/(-t^2-2t+8)

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(dy)/(dt)=-2(t+1)y^2,y(0)=-1/8

\frac{d y}{d t} = - 2 (t + 1) y^{2}, y (0) = - \frac{1}{8}

y = - \frac{1}{- t ^{2} - 2 t + 8}

Solution steps

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

Solve separable ODE:

y = - \frac{1}{- t ^{2} - 2 t + 8}

y = - \frac{1}{- t ^{2} - 2 t + 8}

(y e^{x} + x y e^{x}) d x = - (x e^{x} + 2) d y

\frac{d y}{d x} = \frac{e ^{x}}{e ^{y}}, y (0) = 0

(1 + x^{2}) y^{^{'}} = x^{2} e^{2 y}

y^{^{'}} = - 0.004 y + 50, y (0) = 0

y^{^{'}} = (x + 6) (y - 3), y (0) = 6

What is the solution for (dy)/(dt)=-2(t+1)y^2,y(0)=-1/8 ?
The solution for (dy)/(dt)=-2(t+1)y^2,y(0)=-1/8 is y=-1/(-t^2-2t+8)