12.2.12 problem Problem 15.23

Internal problem ID [3495]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 15, Higher order ordinary differential equations. 15.4 Exercises, page 523
Problem number : Problem 15.23
Date solved : Tuesday, September 30, 2025 at 06:40:48 AM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} \left (x -2\right ) y^{\prime \prime }+3 y^{\prime }+\frac {4 y}{x^{2}}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=(x-2)*diff(diff(y(x),x),x)+3*diff(y(x),x)+4*y(x)/x^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2 \,x^{3}+3 c_1 x -4 c_1}{x \left (x -2\right )^{2}} \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 45

ode=(x-2)*D[y[x],{x,2}]+3*D[y[x],x]+4*y[x]/x^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {6 c_1 x^3+3 c_2 x-4 c_2}{6 \sqrt {2-x} (x-2)^{3/2} x} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x - 2)*Derivative(y(x), (x, 2)) + 3*Derivative(y(x), x) + 4*y(x)/x**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False