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Beliebt Rechnen >

(dy)/(dx)+(1+y^3)/(xy^2(1+x^2))=0

Lösung

\frac{d y}{d x} + \frac{1 + y ^{3}}{x y ^{2} ( 1 + x ^{2} )} = 0

Lösung

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

Schritte zur Lösung

\frac{d y}{d x} + \frac{1 + y ^{3}}{x y ^{2} ( 1 + x ^{2} )} = 0

Solve separable ODE:

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

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

Graph

Beliebte Beispiele

(dy)/(dx)=-2/8 x^6y^2

\frac{d y}{d x} = - \frac{2}{8} x^{6} y^{2}

2x^2+3x^2-2xy(dy)/(dx)=0

2 x^{2} + 3 x^{2} - 2 x y \frac{d y}{d x} = 0

(dP)/(dt)=1.05P(1-P/(7500))

\frac{d P}{d t} = 1.05 P (1 - \frac{P}{7500})

2y(x+1)(dy)/(dx)=2+y^2,y(0)=1

2 y (x + 1) \frac{d y}{d x} = 2 + y^{2}, y (0) = 1

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

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