x^2(dy)/(dx)+1/x y= 2/x y^{-3}

Lösung

x^{2} \frac{d y}{d x} + \frac{1}{x} y = \frac{2}{x} y^{- 3}

y = 4 - e^{\frac{2}{x ^{2}} - c_{1}} + 2, y = - 4 - e^{\frac{2}{x ^{2}} - c_{1}} + 2

Schritte zur Lösung

x^{2} \frac{d y}{d x} + \frac{1}{x} y = \frac{2}{x} y^{- 3}

Solve separable ODE:

y = 4 - e^{\frac{2}{x ^{2}} - c_{1}} + 2, y = - 4 - e^{\frac{2}{x ^{2}} - c_{1}} + 2

y = 4 - e^{\frac{2}{x ^{2}} - c_{1}} + 2, y = - 4 - e^{\frac{2}{x ^{2}} - c_{1}} + 2

\frac{d x}{d y} = 1 - 0.4 x

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

y^{^{'}} = y^{2} x^{2}

\frac{d y}{d x} = 8 x sec (y)

\frac{d y}{d x} = 0.4 x y