y^'=3x^2y,y(1)=1

Lösung

y^{^{'}} = 3 x^{2} y, y (1) = 1

y = e^{x^{3} - 1}

Schritte zur Lösung

y^{'} (x) = 3 x^{2} y

Solve separable ODE:

y = e^{x^{3} - 1}

y = e^{x^{3} - 1}

\frac{d y}{d x} = 3 \frac{x}{x ^{3 + 1}}

y^{^{'}} = 4 t (y - 1)

x (y^{2} + \frac{d y}{d x}) + x^{2} y \frac{d y}{d x} = - y

y^{^{'}} = \frac{y}{25 t ^{2} + 1}

y^{^{'}} = x y + 3 x