What is the solution for (dp)/(dt)=t^2p-7p+t^2-7 ?

The solution for (dp)/(dt)=t^2p-7p+t^2-7 is p=e^{(t^3)/3-7t+c_{1}}-1

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(dp)/(dt)=t^2p-7p+t^2-7

\frac{d p}{d t} = t^{2} p - 7 p + t^{2} - 7

p = e^{\frac{t ^{3}}{3} - 7 t + c_{1}} - 1

Solution steps

\frac{d p}{d t} = t^{2} p - 7 p + t^{2} - 7

Solve separable ODE:

p = e^{\frac{t ^{3}}{3} - 7 t + c_{1}} - 1

p = e^{\frac{t ^{3}}{3} - 7 t + c_{1}} - 1

6 \frac{d y}{d x} + 5 x^{2} y = 97 x^{2}

\frac{d y}{d t} = y \cdot t^{3} - 1.5 \cdot y

y^{^{'}} = \frac{x}{2} - \frac{x}{2} y

\frac{d y}{d x} - \frac{( y ^{2} - y )}{sin ( x )} = 0

y^{^{'}} = - t y^{3}, y (0) = 1

What is the solution for (dp)/(dt)=t^2p-7p+t^2-7 ?
The solution for (dp)/(dt)=t^2p-7p+t^2-7 is p=e^{(t^3)/3-7t+c_{1}}-1