81.12.12 problem 16-13

Internal problem ID [21665]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 16. Variation of Parameters. Page 375.
Problem number : 16-13
Date solved : Thursday, October 02, 2025 at 07:59:37 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} a_{0} \left (x \right ) y^{\prime \prime }+a_{1} \left (x \right ) y^{\prime }+a_{2} \left (x \right ) y&=f \left (x \right ) \end{align*}

✗ Maple

ode:=a__0(x)*diff(diff(y(x),x),x)+a__1(x)*diff(y(x),x)+a__2(x)*y(x) = f(x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=a0[x]*D[y[x],{x,2}]+a1[x]*D[y[x],x]+a2[x]*y[x]==f[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
a0 = Function("a0") 
a1 = Function("a1") 
a2 = Function("a2") 
f = Function("f") 
ode = Eq(a0(x)*Derivative(y(x), (x, 2)) + a1(x)*Derivative(y(x), x) + a2(x)*y(x) - f(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(-a0(x)*Derivative(y(x), (x, 2)) - a2(x)*y(x) + f(x))/a1(x) + Derivative(y(x), x) cannot be solved by the factorable group method