85.1.3 problem 1 (d)

Internal problem ID [22408]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 12
Problem number : 1 (d)
Date solved : Thursday, October 02, 2025 at 08:38:25 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} {s^{\prime \prime \prime }}^{2}+{s^{\prime \prime }}^{3}&=s-3 t \end{align*}

✗ Maple

ode:=diff(diff(diff(s(t),t),t),t)^2+diff(diff(s(t),t),t)^3 = s(t)-3*t; 
dsolve(ode,s(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[s[t],{t,3}]^2+D[s[t],{t,2}]^3==s[t]-3*t; 
ic={}; 
DSolve[{ode,ic},s[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
s = Function("s") 
ode = Eq(3*t - s(t) + Derivative(s(t), (t, 2))**3 + Derivative(s(t), (t, 3))**2,0) 
ics = {} 
dsolve(ode,func=s(t),ics=ics)
 

NotImplementedError : solve: Cannot solve 3*t - s(t) + Derivative(s(t), (t, 2))**3 + Derivative(s(t), (t, 3))**2