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Beliebt Rechnen >

(dP)/(dt)=aP(t)-bP(t)^2

Lösung

\frac{d P}{d t} = a P - b P^{2}

Lösung

P = e^{a t - \frac{b t ^{3}}{3} + c_{1}}

Schritte zur Lösung

\frac{d P}{d t} = a P - b P t^{2}

Solve separable ODE:

P = e^{a t - \frac{b t ^{3}}{3} + c_{1}}

P = e^{a t - \frac{b t ^{3}}{3} + c_{1}}

Graph

Beliebte Beispiele

y - 2 y^{^{'}} + 10 y = 0

(dv)/(dt)=10-1/100 v,v=0,t=0

\frac{d v}{d t} = 10 - \frac{1}{100} v, v = 0, t = 0

(dy)/(dx)=(xsqrt(4-y^2))/(sqrt(1+x^2))

\frac{d y}{d x} = \frac{x 4 - y ^{2}}{1 + x ^{2}}

sqrt(1+x)(dy)/(dx)=sqrt(1+y)

1 + x \frac{d y}{d x} = 1 + y

y^{^{'}} + 17 \frac{y}{x} = 0