23.3.57 problem 59

Internal problem ID [5771]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 59
Date solved : Tuesday, September 30, 2025 at 02:02:53 PM
CAS classification : [_Titchmarsh]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 41

ode:=(a+b)*y(x)/x^2+diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sqrt {x}\, \left (c_1 \,x^{\frac {\sqrt {1-4 a -4 b}}{2}}+c_2 \,x^{-\frac {\sqrt {1-4 a -4 b}}{2}}\right ) \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 61

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

\begin{align*} y(x)&\to x^{\frac {1}{2} \left (1-\sqrt {a+b} \sqrt {\frac {1}{a+b}-4}\right )} \left (c_2 x^{\sqrt {a+b} \sqrt {\frac {1}{a+b}-4}}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.366 (sec). Leaf size: 379

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

\[ \text {Solution too large to show} \]