Internal problem ID [6324]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 34.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {p^{\prime }-a p+b p^{2}=0} \end {gather*} With initial conditions \begin {align*} [p \left (\mathit {t0} \right ) = \mathit {p0}] \end {align*}
✓ Solution by Maple
Time used: 0.049 (sec). Leaf size: 29
dsolve([diff(p(t),t)=a*p(t)-b*p(t)^2,p(t0) = p0],p(t), singsol=all)
\[ p \relax (t ) = \frac {a \mathit {p0}}{\left (-\mathit {p0} b +a \right ) {\mathrm e}^{-a \left (t -\mathit {t0} \right )}+\mathit {p0} b} \]
✓ Solution by Mathematica
Time used: 0.604 (sec). Leaf size: 36
DSolve[{p'[t]==a*p[t]-b*p[t]^2,p[t0]==p0},p[t],t,IncludeSingularSolutions -> True]
\begin{align*} p(t)\to \frac {a \text {p0} e^{a t}}{b \text {p0} e^{a t}+e^{a \text {t0}} (a-b \text {p0})} \\ \end{align*}