59.1.196 problem 198

Internal problem ID [9368]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 198
Date solved : Monday, January 27, 2025 at 06:01:59 PM
CAS classification : [_Gegenbauer]

\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 44

dsolve((1-t^2)*diff(y(t),t$2)-2*t*diff(y(t),t)+6*y(t)=0,y(t), singsol=all)
 

\[ y = \frac {c_{2} \left (3 t^{2}-1\right ) \ln \left (t -1\right )}{2}+\frac {\left (-3 t^{2}+1\right ) c_{2} \ln \left (t +1\right )}{2}-3 c_{1} t^{2}+3 c_{2} t +c_{1} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 55

DSolve[(1-t^2)*D[y[t],{t,2}]-2*t*D[y[t],t]+6*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} c_1 \left (3 t^2-1\right )-\frac {1}{4} c_2 \left (\left (3 t^2-1\right ) \log (1-t)+\left (1-3 t^2\right ) \log (t+1)+6 t\right ) \]