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Beliebt Rechnen >

y(1+x^3)y^'+x^2(1+y^2)=0

Lösung

y (1 + x^{3}) y^{^{'}} + x^{2} (1 + y^{2}) = 0

Lösung

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

Schritte zur Lösung

y (1 + x^{3}) y^{'} (x) + x^{2} (1 + y^{2}) = 0

Solve separable ODE:

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

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

Graph

Beliebte Beispiele

(x(dy))/((dx)-4y)=2x^{(5)}e^{(x)}

\frac{x ( d y )}{( d x ) - 4 y} = 2 x^{(5)} e^{(x)}

\frac{d x}{x} = - v^{2} d v

(dh)/(dt)=-5/(6h^{3/2)}

\frac{d h}{d t} = - \frac{5}{6 h ^{\frac{3}{2}}}

y^{^{'}} - 4 y = 8

(dz)/(dt)=-2e^{t+z}

\frac{d z}{d t} = - 2 e^{t + z}