59.1.664 problem 681

Internal problem ID [9836]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 681
Date solved : Sunday, March 30, 2025 at 02:47:45 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 24

ode:=x^2*diff(diff(y(x),x),x)+2*x^2*diff(y(x),x)+(x-3/4)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {2 c_2 \,{\mathrm e}^{-2 x} x +c_2 \,{\mathrm e}^{-2 x}+c_1}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.208 (sec). Leaf size: 33

ode=x^2*D[y[x],{x,2}]+2*x^2*D[y[x],x]+(x-3/4)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_2 \int _1^xe^{-2 K[1]} K[1]dK[1]+c_1}{\sqrt {x}} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), x) + x**2*Derivative(y(x), (x, 2)) + (x - 3/4)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False