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

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

x y^{^{'}} - 1 = y^{2}

\frac{d y}{d x} = - a y

y^{^{'}} = (2 - y) x, y (1) = - 1

y d x + (2 + x) d y = 0

\frac{d y}{d x} = e^{3 x + 2 y}, y (0) = 0