59.1.320 problem 327

Internal problem ID [9492]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 327
Date solved : Sunday, March 30, 2025 at 02:36:07 PM
CAS classification : [_Laguerre]

\begin{align*} 2 x y^{\prime \prime }-\left (3+2 x \right ) y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.107 (sec). Leaf size: 24

ode:=2*x*diff(diff(y(x),x),x)-(2*x+3)*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{{5}/{2}} \operatorname {hypergeom}\left (\left [2\right ], \left [\frac {7}{2}\right ], x\right )-\frac {2 c_2 \,{\mathrm e}^{x} \left (x -\frac {3}{2}\right )}{3} \]

✓ Mathematica. Time used: 0.9 (sec). Leaf size: 52

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

\[ y(x)\to \frac {1}{2} e^x (2 x-3) \left (c_2 \int _1^x\frac {4 e^{-K[1]} K[1]^{3/2}}{(3-2 K[1])^2}dK[1]+c_1\right ) \]

✗ Sympy

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

False