59.1.507 problem 523

Internal problem ID [9679]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 523
Date solved : Wednesday, March 05, 2025 at 07:57:19 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (3+2 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.071 (sec). Leaf size: 52

ode:=2*x^2*diff(diff(y(x),x),x)+x*(2*x+3)*diff(y(x),x)-(1-x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {3 \left (2 c_{1} \left (-x \right )^{{3}/{2}}+{\mathrm e}^{-x} \left (x c_{1} \sqrt {\pi }\, \operatorname {erf}\left (\sqrt {-x}\right )-\frac {4 c_{2} \sqrt {x}\, \sqrt {-x}}{3}\right )\right )}{4 \sqrt {-x}\, x^{{3}/{2}}} \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 33

ode=2*x^2*D[y[x],{x,2}]+x*(3+2*x)*D[y[x],x]-(1-x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {e^{-x} \left (c_2 x^{3/2} L_{-\frac {3}{2}}^{\frac {3}{2}}(x)+c_1\right )}{x} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) + x*(2*x + 3)*Derivative(y(x), x) - (1 - x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False