10.4.7 problem 9

Internal problem ID [1188]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.5. Page 88
Problem number : 9
Date solved : Monday, January 27, 2025 at 04:43:26 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{2} \left (y^{2}-1\right ) \end{align*}

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 47

dsolve(diff(y(t),t) = y(t)^2*(y(t)^2-1),y(t), singsol=all)
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-\ln \left ({\mathrm e}^{\textit {\_Z}}-2\right ) {\mathrm e}^{\textit {\_Z}}+2 c_1 \,{\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+2 t \,{\mathrm e}^{\textit {\_Z}}+\ln \left ({\mathrm e}^{\textit {\_Z}}-2\right )-2 c_1 -\textit {\_Z} -2 t -2\right )}-1 \]

✓ Solution by Mathematica

Time used: 0.235 (sec). Leaf size: 51

DSolve[D[y[t],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*}