59.1.632 problem 649

Internal problem ID [9804]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 649
Date solved : Monday, January 27, 2025 at 06:14:28 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*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

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

DSolve[t^2*D[y[t],{t,2}]-t*(1+t)*D[y[t],t]+y[t]==0,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*}