62.32.1 problem Ex 1

Internal problem ID [12907]
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 : Monday, March 31, 2025 at 07:24:14 AM
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: 0.427 (sec). Leaf size: 78

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]
 

\[ y(x)\to x^{3/2} \exp \left (\frac {1}{2} \left (2 \int _1^x\frac {K[1]-3}{2 K[1]}dK[1]+x+3\right )\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[2]}\frac {K[1]-3}{2 K[1]}dK[1]\right )dK[2]+c_1\right ) \]

✗ 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