59.1.88 problem 90

Internal problem ID [9260]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 90
Date solved : Sunday, March 30, 2025 at 02:30:54 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (5+x \right ) y^{\prime }-\left (2-3 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 52

ode:=2*x^2*diff(diff(y(x),x),x)+x*(5+x)*diff(y(x),x)-(2-3*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {i \sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}\, \sqrt {x}}{2}\right ) x^{{5}/{2}} {\mathrm e}^{-\frac {x}{2}} c_2 +c_1 \,x^{{5}/{2}} {\mathrm e}^{-\frac {x}{2}}+2 c_2 \left (x^{2}+x +3\right )}{x^{2}} \]

✓ Mathematica. Time used: 0.381 (sec). Leaf size: 94

ode=2*x^2*D[y[x],{x,2}]+x*(5+x)*D[y[x],x]-(2-3*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {e^{-\frac {x}{2}-\frac {5}{4}} \left (15 c_1 x^{5/2}-2 c_2 e^{x/2} x^2-6 c_2 e^{x/2}-2 c_2 e^{x/2} x+\sqrt {2} c_2 (-x)^{5/2} \Gamma \left (\frac {1}{2},-\frac {x}{2}\right )\right )}{15 x^2} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) + x*(x + 5)*Derivative(y(x), x) - (2 - 3*x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False