Internal problem ID [4406]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {s^{\prime }-t \ln \left (s^{2 t}\right )-8 t^{2}=0} \end {gather*}
✗ 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: 0.438 (sec). Leaf size: 34
DSolve[s'[t]==t*Log[s[t]^(2*t)]+8*t^2,s[t],t,IncludeSingularSolutions -> True]
\begin{align*} s(t)\to \text {InverseFunction}\left [\frac {\text {Ei}(\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*}