59.1.254 problem 257

Internal problem ID [9426]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 257
Date solved : Sunday, March 30, 2025 at 02:34:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \end{align*}

✓ Maple. Time used: 0.086 (sec). Leaf size: 45

ode:=2*x*diff(diff(y(x),x),x)+5*(-2*x+1)*diff(y(x),x)-5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {10 \left (\sqrt {5}\, c_1 \sqrt {\pi }\, \left (\frac {1}{10}+x \right ) \operatorname {erfi}\left (\sqrt {5}\, \sqrt {x}\right )-{\mathrm e}^{5 x} c_1 \sqrt {x}-c_2 \left (\frac {1}{10}+x \right )\right )}{x^{{3}/{2}}} \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 40

ode=2*x*D[y[x],{x,2}]+5*(1-2*x)*D[y[x],x]-5*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2 L_{-\frac {1}{2}}^{\frac {3}{2}}(5 x)+\frac {c_1 (10 x+1)}{10 \sqrt {5} x^{3/2}} \]

✗ Sympy

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

False