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

Lösung

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

y = - \frac{- 12 + 144 + 12 ( - c _{1} - 6 x - 2 x ^{3} )}{6}, y = - \frac{- 12 - 144 + 12 ( - c _{1} - 6 x - 2 x ^{3} )}{6}

Schritte zur Lösung

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

Solve separable ODE:

y = - \frac{- 12 + 144 + 12 ( - c _{1} - 6 x - 2 x ^{3} )}{6}, y = - \frac{- 12 - 144 + 12 ( - c _{1} - 6 x - 2 x ^{3} )}{6}

y = - \frac{- 12 + 144 + 12 ( - c _{1} - 6 x - 2 x ^{3} )}{6}, y = - \frac{- 12 - 144 + 12 ( - c _{1} - 6 x - 2 x ^{3} )}{6}

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

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

y^{^{'}} + 14 x y = 0

y y^{^{'}} e^{y^{2}} = x - 1

y^{^{'}} = - y cos (x)