What is the solution for (dv)/(dt)=t^2v-2-2v+t^2 ?

The solution for (dv)/(dt)=t^2v-2-2v+t^2 is v=e^{(t^3)/3-2t+c_{1}}-1

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(dv)/(dt)=t^2v-2-2v+t^2

\frac{d v}{d t} = t^{2} v - 2 - 2 v + t^{2}

v = e^{\frac{t ^{3}}{3} - 2 t + c_{1}} - 1

Solution steps

\frac{d v}{d t} = t^{2} v - 2 - 2 v + t^{2}

Solve separable ODE:

v = e^{\frac{t ^{3}}{3} - 2 t + c_{1}} - 1

v = e^{\frac{t ^{3}}{3} - 2 t + c_{1}} - 1

\frac{d y}{d x} + 100 y = 0

\frac{d y}{d x} = e^{x - y}, y (0) = ln (7)

x^{2} + 4 y \frac{d y}{d x} = 0

(\frac{y}{2 + 6 x}) d x + (ln (x) - 2) d y = 0

\frac{d x}{d t} = 20 - 0.4 \cdot x

What is the solution for (dv)/(dt)=t^2v-2-2v+t^2 ?
The solution for (dv)/(dt)=t^2v-2-2v+t^2 is v=e^{(t^3)/3-2t+c_{1}}-1