59.1.627 problem 644

Internal problem ID [9799]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 644
Date solved : Monday, January 27, 2025 at 06:14:24 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: 20

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

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

✓ Solution by Mathematica

Time used: 0.594 (sec). Leaf size: 54

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

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