(dp)/(dx)=p-p^2

Lösung

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

p = - \frac{e ^{x + c_{1}}}{1 - e ^{x + c_{1}}}

Schritte zur Lösung

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

Solve separable ODE:

p = - \frac{e ^{x + c_{1}}}{1 - e ^{x + c_{1}}}

p = - \frac{e ^{x + c_{1}}}{1 - e ^{x + c_{1}}}

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

e^{x} d x - y d y = 0

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

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

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