78.11.15 problem 10 (c, n=3)

Internal problem ID [18215]
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 : 10 (c, n=3)
Date solved : Monday, March 31, 2025 at 05:22:55 PM
CAS classification : [_Laguerre]

\begin{align*} x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+3 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

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

\[ y = c_1 \,{\mathrm e}^{x}+c_2 \left (x^{3}+3 x^{2}+6 x +6\right ) \]

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 29

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

\[ y(x)\to c_1 e^x-c_2 \left (x^3+3 x^2+6 x+6\right ) \]

✗ Sympy

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

False