59.1.209 problem 212

Internal problem ID [9381]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 212
Date solved : Sunday, March 30, 2025 at 02:33:38 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 34

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

\[ y = t \left (\operatorname {Ei}_{1}\left (-t \right ) {\mathrm e}^{-t} c_2 \,t^{2}+c_1 \,t^{2} {\mathrm e}^{-t}+c_2 t +c_2 \right ) \]

✓ Mathematica. Time used: 48.836 (sec). Leaf size: 50

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

\begin{align*} y(t)\to e^{-t} t^3 \left (\int _1^t\frac {e^{K[1]} c_1}{K[1]^3}dK[1]+c_2\right ) \\ y(t)\to c_2 e^{-t} t^3 \\ \end{align*}

✓ Sympy. Time used: 1.443 (sec). Leaf size: 471

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

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