59.1.209 problem 212

Internal problem ID [9381]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 212
Date solved : Monday, January 27, 2025 at 06:02:07 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*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 34

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

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

✓ Solution by Mathematica

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

DSolve[t^2*D[y[t],{t,2}]+(t^2-3*t)*D[y[t],t]+3*y[t]==0,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*}