87.13.32 problem 36

Internal problem ID [23515]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 100
Problem number : 36
Date solved : Thursday, October 02, 2025 at 09:42:37 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 3 x y^{\prime \prime }-4 y^{\prime }+\frac {5 y}{x}&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 29

ode:=3*x*diff(diff(y(x),x),x)-4*diff(y(x),x)+5*y(x)/x = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{{7}/{6}} \left (c_1 \sin \left (\frac {\sqrt {11}\, \ln \left (x \right )}{6}\right )+c_2 \cos \left (\frac {\sqrt {11}\, \ln \left (x \right )}{6}\right )\right ) \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 42

ode=3*x*D[y[x],{x,2}]-4*D[y[x],x]+5/x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^{7/6} \left (c_2 \cos \left (\frac {1}{6} \sqrt {11} \log (x)\right )+c_1 \sin \left (\frac {1}{6} \sqrt {11} \log (x)\right )\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*Derivative(y(x), x) + 3*Derivative(y(x), (x, 2)) + 5*y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False