59.1.690 problem 707

Internal problem ID [9862]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 707
Date solved : Sunday, March 30, 2025 at 02:48:20 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 35

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

\[ y = \left (\operatorname {Ei}_{1}\left (x \right ) {\mathrm e}^{x} c_2 \,x^{3}+{\mathrm e}^{x} c_1 \,x^{3}-c_2 \left (x^{2}-x +2\right )\right ) x \]

✓ Mathematica. Time used: 60.027 (sec). Leaf size: 39

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

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

✓ Sympy. Time used: 1.379 (sec). Leaf size: 474

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

\[ \text {Solution too large to show} \]