44.12.3 problem 2

Internal problem ID [9293]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.4. THE USE OF A KNOWN SOLUTION TO FIND ANOTHER. Page 74
Problem number : 2
Date solved : Tuesday, September 30, 2025 at 06:16:13 PM
CAS classification : [[_2nd_order, _missing_y]]

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

Using reduction of order method given that one solution is

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 11

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

\[ y = c_1 +\frac {c_2}{x^{2}} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 17

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

\begin{align*} y(x)&\to c_2-\frac {c_1}{2 x^2} \end{align*}

✓ Sympy. Time used: 0.078 (sec). Leaf size: 8

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

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