yy^'=(x^3-2x^2)^2

Lösung

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

y = \frac{2 x ^{7}}{7} - \frac{4 x ^{6}}{3} + \frac{8 x ^{5}}{5} + c_{1}, y = - \frac{2 x ^{7}}{7} - \frac{4 x ^{6}}{3} + \frac{8 x ^{5}}{5} + c_{1}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{2 x ^{7}}{7} - \frac{4 x ^{6}}{3} + \frac{8 x ^{5}}{5} + c_{1}, y = - \frac{2 x ^{7}}{7} - \frac{4 x ^{6}}{3} + \frac{8 x ^{5}}{5} + c_{1}

y = \frac{2 x ^{7}}{7} - \frac{4 x ^{6}}{3} + \frac{8 x ^{5}}{5} + c_{1}, y = - \frac{2 x ^{7}}{7} - \frac{4 x ^{6}}{3} + \frac{8 x ^{5}}{5} + c_{1}

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

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

y^{^{'}} = t^{5} y

\frac{d y}{d x} = x^{5} y, y (1) = 2

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