59.1.243 problem 246

Internal problem ID [9415]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 246
Date solved : Wednesday, March 05, 2025 at 07:48:55 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 29

ode:=x^2*diff(diff(y(x),x),x)-x*(x+3)*diff(y(x),x)+4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.232 (sec). Leaf size: 49

ode=x^2*D[y[x],{x,2}]-x*(x+3)*D[y[x],x]+4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.932 (sec). Leaf size: 430

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - x*(x + 3)*Derivative(y(x), x) + 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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