53.1.201 problem 204

Internal problem ID [10673]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 204
Date solved : Tuesday, September 30, 2025 at 07:30:52 PM
CAS classification : [_Laguerre]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 15

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

\[ y = {\mathrm e}^{t} \left (c_1 \,\operatorname {erf}\left (\sqrt {t}\right )+c_2 \right ) \]

✓ Mathematica. Time used: 0.082 (sec). Leaf size: 21

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

\begin{align*} y(t)&\to e^t \left (c_1-c_2 \Gamma \left (\frac {1}{2},t\right )\right ) \end{align*}

✗ Sympy

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

False