59.1.403 problem 415

Internal problem ID [9575]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 415
Date solved : Sunday, March 30, 2025 at 02:37:51 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 5 y^{\prime \prime }-2 x y^{\prime }+10 y&=0 \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 31

ode:=5*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+10*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \operatorname {hypergeom}\left (\left [-\frac {5}{2}\right ], \left [\frac {1}{2}\right ], \frac {x^{2}}{5}\right )+\frac {4 \left (x^{4}-25 x^{2}+\frac {375}{4}\right ) x c_1}{375} \]

✓ Mathematica. Time used: 0.115 (sec). Leaf size: 138

ode=5*D[y[x],{x,2}]-2*x*D[y[x],x]+10*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {1}{200} \sqrt {\frac {\pi }{5}} c_2 \sqrt {x^2} \left (4 x^4-100 x^2+375\right ) \text {erfi}\left (\frac {\sqrt {x^2}}{\sqrt {5}}\right )+\frac {32 c_1 x^5}{25 \sqrt {5}}-\frac {32 c_1 x^3}{\sqrt {5}}-\frac {9}{20} c_2 e^{\frac {x^2}{5}} x^2+c_2 e^{\frac {x^2}{5}}+\frac {1}{50} c_2 e^{\frac {x^2}{5}} x^4+24 \sqrt {5} c_1 x \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*Derivative(y(x), x) + 10*y(x) + 5*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False