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

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

(x^{2} y - 2 x y) d x + 3 x y^{2} d y = 0

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