(dp)/(dt)=t^2p-3p+t^2-3

Lösung

\frac{d p}{d t} = t^{2} p - 3 p + t^{2} - 3

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

Schritte zur Lösung

\frac{d p}{d t} = t^{2} p - 3 p + t^{2} - 3

Solve separable ODE:

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

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

\frac{d x}{d t} = 3 x

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

\frac{d y}{d x} = - \frac{x}{y e ^{x^{2}}}, y (0) = 1

y^{^{'}} = \frac{1 + y}{1 + x}

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