(dy)/(dx)(3x^2y)=5x^2

Lösung

\frac{d y}{d x} (3 x^{2} y) = 5 x^{2}

y = \frac{10}{3} x + c_{1}, y = - \frac{10}{3} x + c_{1}

Schritte zur Lösung

\frac{d y}{d x} (3 x^{2} y) = 5 x^{2}

Solve separable ODE:

y = \frac{10}{3} x + c_{1}, y = - \frac{10}{3} x + c_{1}

y = \frac{10}{3} x + c_{1}, y = - \frac{10}{3} x + c_{1}

y^{^{'}} = 3 x^{2} (y^{2} + 16), y (0) = 0

x^{2} y^{2} + (1 + y^{2}) y^{^{'}} = 0

(x^{2} - 4) y^{^{'}} - 4 y = 0

\frac{d y}{d x} = x y^{2} + x

\frac{d y}{d x} = - 9 x^{2} y