(dy)/(dx)=(-3x+3xy^2)/(yx^2+2y)

Lösung

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

y = e^{2 c_{1}} x^{6} + 6 e^{2 c_{1}} x^{4} + 12 e^{2 c_{1}} x^{2} + 8 e^{2 c_{1}} + 1, y = - e^{2 c_{1}} x^{6} + 6 e^{2 c_{1}} x^{4} + 12 e^{2 c_{1}} x^{2} + 8 e^{2 c_{1}} + 1

Schritte zur Lösung

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

Solve separable ODE:

y = e^{2 c_{1}} x^{6} + 6 e^{2 c_{1}} x^{4} + 12 e^{2 c_{1}} x^{2} + 8 e^{2 c_{1}} + 1, y = - e^{2 c_{1}} x^{6} + 6 e^{2 c_{1}} x^{4} + 12 e^{2 c_{1}} x^{2} + 8 e^{2 c_{1}} + 1

y = e^{2 c_{1}} x^{6} + 6 e^{2 c_{1}} x^{4} + 12 e^{2 c_{1}} x^{2} + 8 e^{2 c_{1}} + 1, y = - e^{2 c_{1}} x^{6} + 6 e^{2 c_{1}} x^{4} + 12 e^{2 c_{1}} x^{2} + 8 e^{2 c_{1}} + 1

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

\frac{d y}{d x} = - \frac{7 sin ( 3 x )}{2 y}

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

(x^{2} + 9) \frac{d y}{d x} + x y = 0

\frac{d y}{d x} = \frac{6 ( 1 + x )}{x y}