30.1.3 problem 3

Internal problem ID [7393]
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 : Tuesday, September 30, 2025 at 04:30:16 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.135 (sec). Leaf size: 39

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

\begin{align*} s(t)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\log (K[1])+4}dK[1]\&\right ]\left [\frac {2 t^3}{3}+c_1\right ]\\ s(t)&\to \frac {1}{e^4} \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
s = Function("s") 
ode = Eq(-8*t**2 - t*log(s(t)**(2*t)) + Derivative(s(t), t),0) 
ics = {} 
dsolve(ode,func=s(t),ics=ics)
 

NotImplementedError : The given ODE -t*(8*t + log(s(t)**(2*t))) + Derivative(s(t), t) cannot be solved by the factorable group method