56.32.1 problem Ex 1

Internal problem ID [14259]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VIII, Linear differential equations of the second order. Article 55. Summary. Page 129
Problem number : Ex 1
Date solved : Thursday, October 02, 2025 at 09:27:21 AM
CAS classification : [_Laguerre]

\begin{align*} 3 y-\left (x +3\right ) y^{\prime }+x y^{\prime \prime }&=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: 0.047 (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]
 

\begin{align*} y(x)&\to c_1 e^x-c_2 \left (x^3+3 x^2+6 x+6\right ) \end{align*}

✗ 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