86.11.3 problem 3

Internal problem ID [23197]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 9. The operational method. Exercise 9c at page 137
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:24:15 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{4 x^{2}}\right ) y&=\sqrt {x} \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x)+1/x*diff(y(x),x)+(1-1/4/x^2)*y(x) = x^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x +\sin \left (x \right ) c_2 +\cos \left (x \right ) c_1}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.071 (sec). Leaf size: 42

ode=D[y[x],{x,2}]+1/x*D[y[x],x]+(1-1/(4*x^2)) *y[x]==Sqrt[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2 x+2 c_1 e^{-i x}-i c_2 e^{i x}}{2 \sqrt {x}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt(x) + (1 - 1/(4*x**2))*y(x) + Derivative(y(x), (x, 2)) + Derivative(y(x), x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -x**(3/2) + x*y(x) + x*Derivative(y(x), (x, 2)) + Derivative(y(x