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

Lösung

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

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

Schritte zur Lösung

\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

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

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

y^{^{'}} + a y^{2} = 0

\frac{d x}{d t} = 20 - 0.2 \cdot x

\frac{df}{d x} = a_{0} - u f (x)