59.1.633 problem 650

Internal problem ID [9805]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 650
Date solved : Sunday, March 30, 2025 at 02:47:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)+4*x*diff(y(x),x)+(4*x^2+6)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x^{2}} \left (c_1 \cos \left (2 x \right )+c_2 \sin \left (2 x \right )\right ) \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 37

ode=D[y[x],{x,2}]+4*x*D[y[x],x]+(4*x^2+6)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{4} e^{-x (x+2 i)} \left (4 c_1-i c_2 e^{4 i x}\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x*Derivative(y(x), x) + (4*x**2 + 6)*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False