Internal problem ID [1749]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Gegenbauer]
\[ \boxed {\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (t \right ) = \frac {c_{2} \left (3 t^{2}-1\right ) \ln \left (t -1\right )}{2}+\frac {\left (-3 t^{2}+1\right ) c_{2} \ln \left (t +1\right )}{2}-3 c_{1} t^{2}+3 c_{2} t +c_{1} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 55
DSolve[(1-t^2)*y''[t]-2*t*y'[t]+6*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} c_1 \left (3 t^2-1\right )-\frac {1}{4} c_2 \left (\left (3 t^2-1\right ) \log (1-t)+\left (1-3 t^2\right ) \log (t+1)+6 t\right ) \]