Internal problem ID [505]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {t \left (4-y\right ) y}{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 19
dsolve(diff(y(t),t) = 1/3*t*(4-y(t))*y(t),y(t), singsol=all)
\[ y \relax (t ) = \frac {4}{1+4 \,{\mathrm e}^{-\frac {2 t^{2}}{3}} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.268 (sec). Leaf size: 35
DSolve[y'[t]== 1/3*t*(4-y[t])*y[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {4}{1+e^{-\frac {2 t^2}{3}+4 c_1}} \\ y(t)\to 0 \\ y(t)\to 4 \\ \end{align*}