84.26.4 problem 15.9

Internal problem ID [22271]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 15. Variation of parameteres. Supplementary problems
Problem number : 15.9
Date solved : Thursday, October 02, 2025 at 08:36:56 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-\frac {y}{x}&=x^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 42

ode:=diff(diff(y(x),x),x)-y(x)/x = x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sqrt {x}\, \operatorname {BesselI}\left (1, 2 \sqrt {x}\right ) c_2 +\sqrt {x}\, \operatorname {BesselK}\left (1, 2 \sqrt {x}\right ) c_1 -x^{3}-6 x^{2}-12 x \]

✓ Mathematica. Time used: 0.071 (sec). Leaf size: 120

ode=D[y[x],{x,2}]-1/x*y[x]==x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \operatorname {BesselI}\left (1,2 \sqrt {x}\right ) G_{1,3}^{2,1}\left (x\left | \begin {array}{c} \frac {3}{2} \\ \frac {7}{2},\frac {9}{2},\frac {1}{2} \\ \end {array} \right .\right )-\sqrt {x} \left (2 x^{5/2} \operatorname {BesselI}\left (5,2 \sqrt {x}\right ) K_1\left (2 \sqrt {x}\right )+2 (x+6) x^2 \operatorname {BesselI}\left (4,2 \sqrt {x}\right ) K_1\left (2 \sqrt {x}\right )+c_1 \operatorname {BesselI}\left (1,2 \sqrt {x}\right )-2 c_2 K_1\left (2 \sqrt {x}\right )\right ) \end{align*}

✗ Sympy

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

NotImplementedError : solve: Cannot solve -x**2 + Derivative(y(x), (x, 2)) - y(x)/x