87.13.3 problem 3

Internal problem ID [23486]
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 : 3
Date solved : Thursday, October 02, 2025 at 09:42:19 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 3 x^{2} y^{\prime \prime }+4 x y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

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

\[ y = \frac {c_1 \sin \left (\frac {\sqrt {11}\, \ln \left (x \right )}{6}\right )+c_2 \cos \left (\frac {\sqrt {11}\, \ln \left (x \right )}{6}\right )}{x^{{1}/{6}}} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 42

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

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

✓ Sympy. Time used: 0.125 (sec). Leaf size: 34

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

\[ y{\left (x \right )} = \frac {C_{1} \sin {\left (\frac {\sqrt {11} \log {\left (x \right )}}{6} \right )} + C_{2} \cos {\left (\frac {\sqrt {11} \log {\left (x \right )}}{6} \right )}}{\sqrt [6]{x}} \]