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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

Graph

Beliebte Beispiele

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

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

y^'=(xsqrt(x^2-1))/y ,y(-1)=1

y^{^{'}} = \frac{x x ^{2} - 1}{y}, y (- 1) = 1

1/y (dy)/(dx)=(1-2x)

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

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

\frac{d y}{d x} = e^{y}, y = 0, x = 1