Internal problem ID [528]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.4. Page 76
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-t \left (3-y\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve(diff(y(t),t) = t*(3-y(t))*y(t),y(t), singsol=all)
\[ y \relax (t ) = \frac {3}{1+3 \,{\mathrm e}^{-\frac {3 t^{2}}{2}} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.267 (sec). Leaf size: 35
DSolve[y'[t] == t*(3-y[t])*y[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {3}{1+e^{-\frac {3 t^2}{2}+3 c_1}} \\ y(t)\to 0 \\ y(t)\to 3 \\ \end{align*}