Internal problem ID [541]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.5. Page 88
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2} \left (4-y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 49
dsolve(diff(y(t),t) = y(t)^2*(4-y(t)^2),y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{\RootOf \left (\ln \left ({\mathrm e}^{\textit {\_Z}}-4\right ) {\mathrm e}^{\textit {\_Z}}+16 c_{1} {\mathrm e}^{\textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+16 t \,{\mathrm e}^{\textit {\_Z}}-2 \ln \left ({\mathrm e}^{\textit {\_Z}}-4\right )-32 c_{1}+2 \textit {\_Z} -32 t +4\right )}-2 \]
✓ Solution by Mathematica
Time used: 0.259 (sec). Leaf size: 57
DSolve[y'[t] == y[t]^2*(4-y[t]^2),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {InverseFunction}\left [\frac {1}{4 \text {$\#$1}}+\frac {1}{16} \log (2-\text {$\#$1})-\frac {1}{16} \log (\text {$\#$1}+2)\&\right ][-t+c_1] \\ y(t)\to -2 \\ y(t)\to 0 \\ y(t)\to 2 \\ \end{align*}