59.1.208 problem 211

Internal problem ID [9380]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 211
Date solved : Sunday, March 30, 2025 at 02:33:37 PM
CAS classification : [_Laguerre]

\begin{align*} t y^{\prime \prime }-\left (4+t \right ) y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

ode:=t*diff(diff(y(t),t),t)-(4+t)*diff(y(t),t)+2*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 \left (t^{2}+6 t +12\right )+c_2 \,{\mathrm e}^{t} \left (t^{2}-6 t +12\right ) \]

✓ Mathematica. Time used: 0.08 (sec). Leaf size: 87

ode=t*D[y[t],{t,2}]-(4+t)*D[y[t],t]+2*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {2 e^{\frac {t+5}{2}} \sqrt {t} \left (\left (c_2 t^2-6 i c_1 t+12 c_2\right ) \cosh \left (\frac {t}{2}\right )+i \left (c_1 \left (t^2+12\right )+6 i c_2 t\right ) \sinh \left (\frac {t}{2}\right )\right )}{\sqrt {\pi } \sqrt {-i t}} \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t*Derivative(y(t), (t, 2)) - (t + 4)*Derivative(y(t), t) + 2*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

ValueError : Expected Expr or iterable but got None