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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

Graph

Beliebte Beispiele

(2y+3)dy=(x^2+6x)dx

(2 y + 3) d y = (x^{2} + 6 x) d x

(dy)/(dt)=1+t+y^2+ty^2

\frac{d y}{d t} = 1 + t + y^{2} + t y^{2}

2y+3+(2x-4)(dy)/(dx)=0

2 y + 3 + (2 x - 4) \frac{d y}{d x} = 0

(x-1)((dy)/(dx))=(4-y^2)

(x - 1) (\frac{d y}{d x}) = (4 - y^{2})

3xy^'-2y=0,y(0)=x^{2/3}

3 x y^{^{'}} - 2 y = 0, y (0) = x^{\frac{2}{3}}