Internal problem ID [1953]
Book: Ordinary Differential Equations, Robert H. Martin, 1983
Section: Problem 1.1-5, page 7
Problem number: 1.1-5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2}+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve(diff(y(t),t)=y(t)^2-y(t),y(t), singsol=all)
\[ y \relax (t ) = \frac {1}{1+c_{1} {\mathrm e}^{t}} \]
✓ Solution by Mathematica
Time used: 0.243 (sec). Leaf size: 25
DSolve[y'[t]==y[t]^2-y[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{1+e^{t+c_1}} \\ y(t)\to 0 \\ y(t)\to 1 \\ \end{align*}