59.1.246 problem 249

Internal problem ID [9418]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 249
Date solved : Wednesday, March 05, 2025 at 07:48:58 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 41

ode:=x^2*diff(diff(y(x),x),x)+x*(5-x)*diff(y(x),x)+4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (x^{2}-4 x +2\right ) c_{2} \operatorname {Ei}_{1}\left (-x \right )+c_{2} \left (x -3\right ) {\mathrm e}^{x}+c_{1} \left (x^{2}-4 x +2\right )}{x^{2}} \]

✓ Mathematica. Time used: 0.358 (sec). Leaf size: 51

ode=x^2*D[y[x],{x,2}]+x*(5-x)*D[y[x],x]+4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\left (x^2-4 x+2\right ) \left (c_2 \int _1^x\frac {e^{K[1]}}{K[1] \left (K[1]^2-4 K[1]+2\right )^2}dK[1]+c_1\right )}{x^2} \]

✓ Sympy. Time used: 1.820 (sec). Leaf size: 430

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + x*(5 - x)*Derivative(y(x), x) + 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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