88.21.2 problem 2

Internal problem ID [24152]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Exercises at page 149
Problem number : 2
Date solved : Thursday, October 02, 2025 at 10:00:15 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

Using reduction of order method given that one solution is

\begin{align*} y&=\frac {1}{x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 17

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

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

✓ Sympy. Time used: 0.100 (sec). Leaf size: 10

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

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