59.1.194 problem 196

Internal problem ID [9366]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 196
Date solved : Monday, January 27, 2025 at 06:01:57 PM
CAS classification : [_Gegenbauer]

\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 33

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

\[ y(t)\to c_1 t-\frac {1}{2} c_2 (t \log (1-t)-t \log (t+1)+2) \]