Internal problem ID [4914]
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')`]
\[ \boxed {s^{\prime }-t \ln \left (s^{2 t}\right )=8 t^{2}} \]
✗ 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: 0.28 (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 {\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*}