78.11.3 problem 3

Internal problem ID [18195]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 16. The Use of a Known Solution to find Another. Problems at page 121
Problem number : 3
Date solved : Thursday, March 13, 2025 at 11:48:51 AM
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: 0.003 (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: 0.009 (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]
 

\[ y(x)\to c_2-\frac {c_1}{2 x^2} \]

✓ Sympy. Time used: 0.131 (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)
 

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