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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

Graph

Beliebte Beispiele

(dy)/(dx)+2/x y= 3/x

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

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

(dy)/(dt)-2t*y=t

\frac{d y}{d t} - 2 t \cdot y = t

(dy)/(dt)=2sqrt(y)sqrt(t),y(1)=7

\frac{d y}{d t} = 2 y t, y (1) = 7

e^{-y}dx+(1+x^2)dy=0

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