Internal problem ID [538]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.5. Page 88
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2} \left (y^{2}-1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.053 (sec). Leaf size: 47
dsolve(diff(y(t),t) = y(t)^2*(y(t)^2-1),y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{\RootOf \left (-\ln \left ({\mathrm e}^{\textit {\_Z}}-2\right ) {\mathrm e}^{\textit {\_Z}}+2 c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+2 t \,{\mathrm e}^{\textit {\_Z}}+\ln \left ({\mathrm e}^{\textit {\_Z}}-2\right )-2 c_{1}-\textit {\_Z} -2 t -2\right )}-1 \]
✓ Solution by Mathematica
Time used: 0.233 (sec). Leaf size: 51
DSolve[y'[t] == y[t]^2*(y[t]^2-1),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {InverseFunction}\left [\frac {1}{\text {$\#$1}}+\frac {1}{2} \log (1-\text {$\#$1})-\frac {1}{2} \log (\text {$\#$1}+1)\&\right ][t+c_1] \\ y(t)\to -1 \\ y(t)\to 0 \\ y(t)\to 1 \\ \end{align*}