Internal problem ID [1956]
Book: Ordinary Differential Equations, Robert H. Martin, 1983
Section: Problem 1.1-6, page 7
Problem number: 1.1-6 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-y^{3}+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 16
dsolve(diff(y(t),t)=y(t)^3-y(t)^2,y(t), singsol=all)
\[ y \relax (t ) = \frac {1}{\LambertW \left (-c_{1} {\mathrm e}^{t -1}\right )+1} \]
✓ Solution by Mathematica
Time used: 0.229 (sec). Leaf size: 38
DSolve[y'[t]==y[t]^3-y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {InverseFunction}\left [\frac {1}{\text {$\#$1}}+\log (1-\text {$\#$1})-\log (\text {$\#$1})\&\right ][t+c_1] \\ y(t)\to 0 \\ y(t)\to 1 \\ \end{align*}