53.1.290 problem 293

Internal problem ID [10762]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 293
Date solved : Tuesday, September 30, 2025 at 07:31:44 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.034 (sec). Leaf size: 29

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

\[ y = 2 \left (x -\frac {3}{2}\right ) c_1 \left (2 x -3\right )^{{3}/{4}} \operatorname {KummerM}\left (\frac {3}{4}, \frac {11}{4}, \frac {x}{2}-\frac {3}{4}\right )+c_2 x \]

✓ Mathematica. Time used: 0.051 (sec). Leaf size: 63

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

\begin{align*} y(x)&\to 2\ 2^{3/4} (2 x-3) \left (c_2 (2 x-3)^{3/4} L_{-\frac {3}{4}}^{\frac {7}{4}}\left (\frac {x}{2}-\frac {3}{4}\right )+\frac {4 \sqrt {2} c_1 x}{2 x-3}\right ) \end{align*}

✗ Sympy

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

False