What is the solution for (dp)/(dt)=t^2p-8p+t^2-8 ?

The solution for (dp)/(dt)=t^2p-8p+t^2-8 is p=e^{(t^3)/3-8t+c_{1}}-1

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(dp)/(dt)=t^2p-8p+t^2-8

\frac{d p}{d t} = t^{2} p - 8 p + t^{2} - 8

p = e^{\frac{t ^{3}}{3} - 8 t + c_{1}} - 1

Solution steps

\frac{d p}{d t} = t^{2} p - 8 p + t^{2} - 8

Solve separable ODE:

p = e^{\frac{t ^{3}}{3} - 8 t + c_{1}} - 1

p = e^{\frac{t ^{3}}{3} - 8 t + c_{1}} - 1

(x^{2} + 1) d x + \frac{1}{y} d y = 0

10 x^{2} y + 2 x^{3} y^{^{'}} - 16 y = 0

1 = y^{^{'}} e^{y} x

\frac{d y}{d x} = \frac{y x + 3 x - y - 3}{x y - 2 x + 4 y - 8}

\frac{d y}{d x} = \frac{9 ( 1 + x )}{x y}

What is the solution for (dp)/(dt)=t^2p-8p+t^2-8 ?
The solution for (dp)/(dt)=t^2p-8p+t^2-8 is p=e^{(t^3)/3-8t+c_{1}}-1