What is the solution for (dy)/(dt)=([3t^2+4t+2])/([2y-2]),y(0)=-1 ?

The solution for (dy)/(dt)=([3t^2+4t+2])/([2y-2]),y(0)=-1 is y=1-sqrt((t^2+2)(t+2))

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(dy)/(dt)=([3t^2+4t+2])/([2y-2]),y(0)=-1

\frac{d y}{d t} = \frac{[ 3 t ^{2} + 4 t + 2 ]}{[ 2 y - 2 ]}, y (0) = - 1

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

Solution steps

\frac{d y}{d t} = \frac{[ 3 t ^{2} + 4 t + 2 ]}{[ 2 y - 2 ]}

Solve separable ODE:

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

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

y^{^{'}} = \frac{8 ( 1 + x )}{x y}

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

\frac{d x}{d y} = e^{x - y}

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

- \frac{x}{y} = y^{^{'}}

What is the solution for (dy)/(dt)=([3t^2+4t+2])/([2y-2]),y(0)=-1 ?
The solution for (dy)/(dt)=([3t^2+4t+2])/([2y-2]),y(0)=-1 is y=1-sqrt((t^2+2)(t+2))