10.2.27 problem 27

Internal problem ID [1155]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 27
Date solved : Monday, January 27, 2025 at 04:37:06 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(diff(y(t),t) = 1/3*t*(4-y(t))*y(t),y(t), singsol=all)
 

\[ y = \frac {4}{1+4 \,{\mathrm e}^{-\frac {2 t^{2}}{3}} c_1} \]

✓ Solution by Mathematica

Time used: 0.249 (sec). Leaf size: 44

DSolve[D[y[t],t]== 1/3*t*(4-y[t])*y[t],y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {4 e^{\frac {2 t^2}{3}}}{e^{\frac {2 t^2}{3}}+e^{4 c_1}} \\ y(t)\to 0 \\ y(t)\to 4 \\ \end{align*}