84.18.8 problem 10.16

Internal problem ID [22205]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 10. Linear differential equations. General remarks. Supplementary problems
Problem number : 10.16
Date solved : Thursday, October 02, 2025 at 08:36:09 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime }+y&=5 \sin \left (x \right ) \end{align*}

✗ Maple

ode:=diff(diff(diff(y(x),x),x),x)+(x^2-1)*diff(diff(y(x),x),x)-2*diff(y(x),x)+y(x) = 5*sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,3}]+(x^2-1)*D[y[x],{x,2}]-2*D[y[x],{x,1}]+y[x]==5*Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x**2 - 1)*Derivative(y(x), (x, 2)) + y(x) - 5*sin(x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -x**2*Derivative(y(x), (x, 2))/2 - y(x)/2 + 5*sin(x)/2 + Derivative(y(x), x) + Derivative(y(x), (x, 2))/2 - Derivative(y(x), (x, 3))/2 cannot be solved by the factorable group method