59.1.410 problem 422

Internal problem ID [9582]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 422
Date solved : Monday, January 27, 2025 at 06:04:20 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 17

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

\[ y(t)\to e t \left (c_2 e^t+c_1\right ) \]