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Beliebt Rechnen >

(x^2-1)y^'+xy(1-y)=0

Lösung

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

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

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

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

(dx)/(dt)=e^xtcos(t)

\frac{d x}{d t} = e^{x} t cos (t)

(dy)/(dx)+9x^2y=27x^2

\frac{d y}{d x} + 9 x^{2} y = 27 x^{2}

(dx)/(dt)=18-18/100 x

\frac{d x}{d t} = 18 - \frac{18}{100} x

3.03y^'+0.755y=6.05

3.03 y^{^{'}} + 0.755 y = 6.05

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

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