y^'+3x^2*y=x^2

Lösung

y^{^{'}} + 3 x^{2} \cdot y = x^{2}

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

Schritte zur Lösung

y^{'} (x) + 3 x^{2} \cdot y = x^{2}

Solve separable ODE:

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

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

\frac{d y}{d x} 3 x^{2} y = 6 x^{2}

\frac{d y}{d x} + 2 y = 11, y (0) = 1

y^{^{'}} + 3 y = 12

\frac{d y}{d x} = - 2 y + 3

x^{^{'}} = x (1 - x), x (0) = 10