78.2.22 problem 8.a

Internal problem ID [20974]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 2, Second order ODEs. Problems section 2.6
Problem number : 8.a
Date solved : Thursday, October 02, 2025 at 07:00:52 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to \frac {c_2 \cos (\log (x))+c_1 \sin (\log (x))}{x} \end{align*}

✓ Sympy. Time used: 0.108 (sec). Leaf size: 17

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

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