36.1.3 problem 3

Internal problem ID [6258]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page 46
Problem number : 3
Date solved : Monday, January 27, 2025 at 01:50:17 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} s^{\prime }&=t \ln \left (s^{2 t}\right )+8 t^{2} \end{align*}

✗ Solution by Maple

dsolve(diff(s(t),t)=t*ln(s(t)^(2*t))+8*t^2,s(t), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.326 (sec). Leaf size: 34

DSolve[D[s[t],t]==t*Log[s[t]^(2*t)]+8*t^2,s[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} s(t)\to \text {InverseFunction}\left [\frac {\operatorname {ExpIntegralEi}(\log (\text {$\#$1})+4)}{e^4}\&\right ]\left [\frac {2 t^3}{3}+c_1\right ] \\ s(t)\to \frac {1}{e^4} \\ \end{align*}