y^'=2x^2y

Lösung

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

y = e^{\frac{2 x ^{3}}{3} + c_{1}}

Schritte zur Lösung

y^{'} (x) = 2 x^{2} y

Solve separable ODE:

y = e^{\frac{2 x ^{3}}{3} + c_{1}}

y = e^{\frac{2 x ^{3}}{3} + c_{1}}

e^{2 x} (2 cos (y) d x - sin (y) d y) = 0

3 (1 + t^{2}) y^{^{'}} = 2 t y (y^{3} - 1)

\frac{d y}{d x} = 2 x y - x

\frac{d y}{d x} = - 0.01 y

\frac{d y}{d t} + 2 t y = t