59.1.438 problem 451

Internal problem ID [9610]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 451
Date solved : Wednesday, March 05, 2025 at 07:51:37 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x y^{\prime \prime }+\left (4 x +1\right ) y^{\prime }+\left (2 x +1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 16

ode:=2*x*diff(diff(y(x),x),x)+(4*x+1)*diff(y(x),x)+(2*x+1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} \left (c_{1} +c_{2} \sqrt {x}\right ) \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 23

ode=2*x*D[y[x],{x,2}]+(4*x+1)*D[y[x],x]+(2*x+1)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-x} \left (2 c_2 \sqrt {x}+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*Derivative(y(x), (x, 2)) + (2*x + 1)*y(x) + (4*x + 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False