10.2.28 problem 28

Internal problem ID [1156]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 28
Date solved : Monday, January 27, 2025 at 04:37:08 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 22

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

\[ y = \frac {4}{1+4 \,{\mathrm e}^{-4 t} \left (t +1\right )^{4} c_1} \]

✓ Solution by Mathematica

Time used: 3.294 (sec). Leaf size: 42

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

\begin{align*} y(t)\to \frac {4 e^{4 t}}{e^{4 t}+e^{4 c_1} (t+1)^4} \\ y(t)\to 0 \\ y(t)\to 4 \\ \end{align*}