Internal problem ID [8261]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 788.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Gegenbauer]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 73
dsolve((1-x^2)*diff(y(x),x$2)-2*x*diff(y(x),x)+30*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (\frac {21}{5} x^{5}-\frac {14}{3} x^{3}+x \right )+c_{2} \left (\frac {1}{225}+\frac {\left (63 x^{5}-70 x^{3}+15 x \right ) \ln \left (x -1\right )}{1920}+\frac {\left (-63 x^{5}+70 x^{3}-15 x \right ) \ln \left (x +1\right )}{1920}+\frac {21 x^{4}}{320}-\frac {49 x^{2}}{960}\right ) \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 76
DSolve[(1-x^2)*y''[x]-2*x*y'[x]+30*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8} c_1 x \left (63 x^4-70 x^2+15\right )+c_2 \left (-\frac {63 x^4}{8}+\frac {49 x^2}{8}-\frac {1}{16} \left (63 x^4-70 x^2+15\right ) x (\log (1-x)-\log (x+1))-\frac {8}{15}\right ) \]