xyy^'=1-x^3

Lösung

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

y = \frac{6 ln ( x ) - 2 x ^{3} + c _{1}}{3}, y = - \frac{6 ln ( x ) - 2 x ^{3} + c _{1}}{3}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{6 ln ( x ) - 2 x ^{3} + c _{1}}{3}, y = - \frac{6 ln ( x ) - 2 x ^{3} + c _{1}}{3}

y = \frac{6 ln ( x ) - 2 x ^{3} + c _{1}}{3}, y = - \frac{6 ln ( x ) - 2 x ^{3} + c _{1}}{3}

\frac{d y}{d x} = 6 x y + 8 y

\frac{y ^{^{'}}}{x} - \frac{e ^{x}}{y} = 0

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

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

y^{^{'}} + n^{2} y - y = a