87.9.17 problem 32

Internal problem ID [23390]
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 74
Problem number : 32
Date solved : Thursday, October 02, 2025 at 09:40:58 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: 0.024 (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: 0.277 (sec). Leaf size: 114

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)) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt {x + 3} \left (C_{1} \left (- \frac {x}{x + 3} + 1\right )^{\sqrt {7} i} {{}_{2}F_{1}\left (\begin {matrix} - \frac {1}{2} + \frac {\sqrt {7} i}{2}, \frac {1}{2} + \frac {\sqrt {7} i}{2} \\ 1 + \sqrt {7} i \end {matrix}\middle | {- \frac {x}{x + 3} + 1} \right )} + C_{2} {{}_{2}F_{1}\left (\begin {matrix} - \frac {1}{2} - \frac {\sqrt {7} i}{2}, \frac {1}{2} - \frac {\sqrt {7} i}{2} \\ 1 - \sqrt {7} i \end {matrix}\middle | {- \frac {x}{x + 3} + 1} \right )}\right ) e^{\frac {\sqrt {7} i \log {\left (x + 3 \right )}}{2}} \]