87.13.17 problem 18

Internal problem ID [23500]
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 : 18
Date solved : Thursday, October 02, 2025 at 09:42:30 PM
CAS classification : [[_Emden, _Fowler]]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ y^{\prime }\left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 11

ode:=x^2*diff(diff(y(x),x),x)+3*x*diff(y(x),x)+2*y(x) = 0; 
ic:=[y(1) = 0, D(y)(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\sin \left (\ln \left (x \right )\right )}{x} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 12

ode=x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+2*y[x]==0; 
ic={y[1]==0,Derivative[1][y][1] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.126 (sec). Leaf size: 8

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 = {y(1): 0, Subs(Derivative(y(x), x), x, 1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\sin {\left (\log {\left (x \right )} \right )}}{x} \]