10.3.13 problem 17

Internal problem ID [1178]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 17
Date solved : Monday, January 27, 2025 at 04:39:29 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=t \left (3-y\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

dsolve(diff(y(t),t) = t*(3-y(t))*y(t),y(t), singsol=all)
 

\[ y = \frac {3}{1+3 \,{\mathrm e}^{-\frac {3 t^{2}}{2}} c_1} \]

✓ Solution by Mathematica

Time used: 0.232 (sec). Leaf size: 44

DSolve[D[y[t],t] == t*(3-y[t])*y[t],y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {3 e^{\frac {3 t^2}{2}}}{e^{\frac {3 t^2}{2}}+e^{3 c_1}} \\ y(t)\to 0 \\ y(t)\to 3 \\ \end{align*}