64.22.11 problem 4(d)

Internal problem ID [13605]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 11, The nth order homogeneous linear differential equation. Section 11.8, Exercises page 583
Problem number : 4(d)
Date solved : Monday, March 31, 2025 at 08:02:28 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} f \left (t \right ) x^{\prime \prime }+g \left (t \right ) x&=0 \end{align*}

✗ Maple

ode:=f(t)*diff(diff(x(t),t),t)+g(t)*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=f[t]*D[x[t],{t,2}]+g[t]*x[t]==0; 
ic={}; 
DSolve[{ode,ic},{x[t]},t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(f(t)*Derivative(x(t), (t, 2)) + g(t)*x(t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

TypeError : cannot determine truth value of Relational