59.1.245 problem 248

Internal problem ID [9417]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 248
Date solved : Sunday, March 30, 2025 at 02:34:29 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 48

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

\[ y = \frac {x^{3} c_2 \,{\mathrm e}^{x} \left (x +4\right ) \operatorname {Ei}_{1}\left (x \right )+c_1 \,x^{3} {\mathrm e}^{x} \left (x +4\right )-c_2 \left (x^{3}+3 x^{2}-2 x +2\right )}{x} \]

✓ Mathematica. Time used: 0.305 (sec). Leaf size: 45

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

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

✗ Sympy

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

False