80.5.54 problem D 4

Internal problem ID [21275]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 5. Second order equations. Excercise 5.9 at page 119
Problem number : D 4
Date solved : Thursday, October 02, 2025 at 07:27:35 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }-p \left (t \right ) x&=q \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (a \right )&=0 \\ x \left (b \right )&=0 \\ \end{align*}

✗ Maple

ode:=diff(diff(x(t),t),t)-p(t)*x(t) = q(t); 
ic:=[x(a) = 0, x(b) = 0]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[x[t],{t,2}]-p[t]*x[t]==q[t]; 
ic={x[a]==0,x[b]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
a = symbols("a") 
b = symbols("b") 
x = Function("x") 
p = Function("p") 
q = Function("q") 
ode = Eq(-p(t)*x(t) - q(t) + Derivative(x(t), (t, 2)),0) 
ics = {x(a): 0, x(b): 0} 
dsolve(ode,func=x(t),ics=ics)
 

NotImplementedError : solve: Cannot solve -p(t)*x(t) - q(t) + Derivative(x(t), (t, 2))