10.4.11 problem 13

Internal problem ID [1192]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.5. Page 88
Problem number : 13
Date solved : Monday, January 27, 2025 at 04:43:37 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 66

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

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

✓ Solution by Mathematica

Time used: 0.339 (sec). Leaf size: 50

DSolve[D[y[t],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*}