59.1.632 problem 649

Internal problem ID [9804]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 649
Date solved : Sunday, March 30, 2025 at 02:47:00 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 15

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

\[ y = {\mathrm e}^{t} t \left (\operatorname {Ei}_{1}\left (t \right ) c_2 +c_1 \right ) \]

✓ Mathematica. Time used: 35.564 (sec). Leaf size: 44

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

\begin{align*} y(t)\to e^t t \left (\int _1^t\frac {e^{-K[1]} c_1}{K[1]}dK[1]+c_2\right ) \\ y(t)\to c_2 e^t t \\ \end{align*}

✓ Sympy. Time used: 2.007 (sec). Leaf size: 430

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

\[ \text {Solution too large to show} \]