(dy)/(dx)=2y(1-y/5)

Lösung

\frac{d y}{d x} = 2 y (1 - \frac{y}{5})

y = - \frac{5 e ^{2 x + c_{1}}}{1 - e ^{2 x + c_{1}}}

Schritte zur Lösung

\frac{d y}{d x} = 2 y (1 - \frac{y}{5})

Solve separable ODE:

y = - \frac{5 e ^{2 x + c_{1}}}{1 - e ^{2 x + c_{1}}}

y = - \frac{5 e ^{2 x + c_{1}}}{1 - e ^{2 x + c_{1}}}

x e^{x^{2}} + y y^{^{'}} = 0

y^{^{'}} = e^{y} sin (x)

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

10 y^{2} (x d y + y d x) = y d x - x d y

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