76.1.35 problem 35

Internal problem ID [17334]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 35
Date solved : Tuesday, January 28, 2025 at 10:01:30 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 18

dsolve([diff(y(t),t)=t*y(t)*(4-y(t))/3,y(0) = 1/2],y(t), singsol=all)
 

\[ y = \frac {4}{1+7 \,{\mathrm e}^{-\frac {2 t^{2}}{3}}} \]

✓ Solution by Mathematica

Time used: 0.260 (sec). Leaf size: 29

DSolve[{D[y[t],t]==t*y[t]*(4-y[t])/3,{y[0]==1/2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {4 e^{\frac {2 t^2}{3}}}{e^{\frac {2 t^2}{3}}+7} \]