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Beliebt Rechnen >

y^'=(1+y^2)/(xy(1+x^2))

Lösung

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

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

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

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^{^{'}} = \frac{y + 1}{x}

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

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

3e^xtan(y)dx+(1-e^x)sec^2(y)dy=0

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

(dy)/(dx)=ye^{3x}

\frac{d y}{d x} = y e^{3 x}

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

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