59.1.445 problem 458

Internal problem ID [9617]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 458
Date solved : Wednesday, March 05, 2025 at 07:51:41 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 25

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

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

✗ Sympy

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

False