Internal problem ID [542]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.5. Page 88
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-\left (1-y\right )^{2} y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.029 (sec). Leaf size: 66
dsolve(diff(y(t),t) = (1-y(t))^2*y(t)^2,y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{\RootOf \left (-2 \ln \left ({\mathrm e}^{\textit {\_Z}}+1\right ) {\mathrm e}^{2 \textit {\_Z}}+c_{1} {\mathrm e}^{2 \textit {\_Z}}+2 \textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}+t \,{\mathrm e}^{2 \textit {\_Z}}-2 \ln \left ({\mathrm e}^{\textit {\_Z}}+1\right ) {\mathrm e}^{\textit {\_Z}}+c_{1} {\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+t \,{\mathrm e}^{\textit {\_Z}}+2 \,{\mathrm e}^{\textit {\_Z}}+1\right )}+1 \]
✓ Solution by Mathematica
Time used: 0.385 (sec). Leaf size: 50
DSolve[y'[t] == (1-y[t])^2*y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {InverseFunction}\left [-\frac {1}{\text {$\#$1}-1}-\frac {1}{\text {$\#$1}}-2 \log (1-\text {$\#$1})+2 \log (\text {$\#$1})\&\right ][t+c_1] \\ y(t)\to 0 \\ y(t)\to 1 \\ \end{align*}