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Beliebt Rechnen >

(dy)/(dx)-(xy)/(1-x^2)=(xy^2)/(1-x^2)

Lösung

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

Lösung

y = \frac{e ^{c_{1}} ( ( - x ^{2} + 1 ) ^{\frac{1}{2}} + e ^{c_{1}} )}{- x ^{2} + 1 - e ^{2 c_{1}}}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{e ^{c_{1}} ( ( - x ^{2} + 1 ) ^{\frac{1}{2}} + e ^{c_{1}} )}{- x ^{2} + 1 - e ^{2 c_{1}}}

y = \frac{e ^{c_{1}} ( ( - x ^{2} + 1 ) ^{\frac{1}{2}} + e ^{c_{1}} )}{- x ^{2} + 1 - e ^{2 c_{1}}}

Graph

Beliebte Beispiele

ye^x(dy)/(dx)=e^{-y}+e^{-2x-y}

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

x(dy)/(dx)=y^2-9

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

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

(x^2+9)(dy)/(dx)=xy

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

y^'=xy^2sin(x^2),y(0)=1

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