90.20.39 problem 26 and 27

Internal problem ID [25334]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 5. Second Order Linear Differential Equations. Exercises at page 337
Problem number : 26 and 27
Date solved : Friday, October 03, 2025 at 12:00:18 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+a_{1} \left (t \right ) y^{\prime }+a_{0} \left (t \right ) y&=f \left (t \right ) \end{align*}

✗ Maple

ode:=diff(diff(y(t),t),t)+a__1(t)*diff(y(t),t)+a__0(t)*y(t) = f(t); 
dsolve(ode,y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[t],{t,2}]+a1[t]*D[y[t],t]+a0[t]*y[t]==f[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
a1 = Function("a1") 
a0 = Function("a0") 
ode = Eq(a0(t)*y(t) + a1(t)*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

TypeError : cannot determine truth value of Relational: _n < t