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Beliebt Rechnen >

(xdx)/(1+x^2)+(ydy)/(1+y^2)=0

Lösung

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

Lösung

y = \frac{c _{1} - x ^{2} - 1}{x ^{2} + 1}, y = - \frac{c _{1} - x ^{2} - 1}{x ^{2} + 1}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{c _{1} - x ^{2} - 1}{x ^{2} + 1}, y = - \frac{c _{1} - x ^{2} - 1}{x ^{2} + 1}

y = \frac{c _{1} - x ^{2} - 1}{x ^{2} + 1}, y = - \frac{c _{1} - x ^{2} - 1}{x ^{2} + 1}

Graph

Beliebte Beispiele

(dx)/(dt)=t*x^{1/2}

\frac{d x}{d t} = t \cdot x^{\frac{1}{2}}

(dy)/(dx)=(cos^2(y))/(4x-3)

\frac{d y}{d x} = \frac{cos ^{2} ( y )}{4 x - 3}

(dy)/(dx)+2xyy=0,y(0)=-1

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

(x^2-x^2y)dy+2xydx=0

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

(dy)/(dx)=8xsqrt(9-y^2)

\frac{d y}{d x} = 8 x 9 - y^{2}