y^2y^'=x^2+6e^x

Lösung

y^{2} y^{^{'}} = x^{2} + 6 e^{x}

y = 3 x^{3} + 18 e^{x} + c_{1}

Schritte zur Lösung

y^{2} y^{'} (x) = x^{2} + 6 e^{x}

Solve separable ODE:

y = 3 x^{3} + 18 e^{x} + c_{1}

y = 3 x^{3} + 18 e^{x} + c_{1}

y^{^{'}} + y = 0, y (1) = 1

x (3 y^{2} - 2) y^{^{'}} (x) - y^{3} = 0, y (1) = 2

y^{2} d y = x d x

tan^{2} (x) cos^{2} (y) d x = d y

\frac{d y}{d x} = \frac{- 6}{4} x^{5} y^{8}