76.1.36 problem 36

Internal problem ID [17335]
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 : 36
Date solved : Tuesday, January 28, 2025 at 10:01:33 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {t y \left (4-y\right )}{1+t} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 20

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

\[ y = \frac {4}{1+{\mathrm e}^{-4 t} \left (t +1\right )^{4}} \]

✓ Solution by Mathematica

Time used: 3.300 (sec). Leaf size: 25

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

\[ y(t)\to \frac {4 e^{4 t}}{(t+1)^4+e^{4 t}} \]