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

Lösung

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

y = W (\frac{1}{e ^{\frac{- x ^{2} - c _{1}}{2}}})

Schritte zur Lösung

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

Solve separable ODE:

y = W (\frac{1}{e ^{\frac{- x ^{2} - c _{1}}{2}}})

y = W (\frac{1}{e ^{\frac{- x ^{2} - c _{1}}{2}}})

y^{^{'}} = u - y

y^{^{'}} = y^{2} + 2 y + 1

\frac{y ^{^{'}}}{x} = 4 y

y^{3} \frac{d y}{d x} = - x^{4}

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