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

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

Graph

Beliebte Beispiele

(df)/(dx)=-f(x)

\frac{df}{d x} = - f (x)

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

(dy)/(dx)=x*e^y,y(2)=0

\frac{d y}{d x} = x \cdot e^{y}, y (2) = 0

(dp)/(dt)=0.2p-380

\frac{d p}{d t} = 0.2 p - 380

4y^'-3y-83=3y^'

4 y^{^{'}} - 3 y - 83 = 3 y^{^{'}}