59.1.235 problem 238

Internal problem ID [9407]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 238
Date solved : Sunday, March 30, 2025 at 02:34:16 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x \left (3-x \right ) y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 28

ode:=x^2*diff(diff(y(x),x),x)+x*(-x+3)*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.415 (sec). Leaf size: 40

ode=x^2*D[y[x],{x,2}]+x*(3-x)*D[y[x],x]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.947 (sec). Leaf size: 430

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + x*(3 - x)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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