59.1.766 problem 788

Internal problem ID [9938]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 788
Date solved : Monday, January 27, 2025 at 06:15:58 PM
CAS classification : [_Gegenbauer]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 71

dsolve((1-x^2)*diff(y(x),x$2)-2*x*diff(y(x),x)+30*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {21 c_{2} x \left (x^{4}-\frac {10}{9} x^{2}+\frac {5}{21}\right ) \ln \left (x -1\right )}{640}-\frac {21 c_{2} x \left (x^{4}-\frac {10}{9} x^{2}+\frac {5}{21}\right ) \ln \left (x +1\right )}{640}+\frac {21 c_{1} x^{5}}{5}+\frac {21 c_{2} x^{4}}{320}-\frac {14 c_{1} x^{3}}{3}-\frac {49 c_{2} x^{2}}{960}+c_{1} x +\frac {c_{2}}{225} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 76

DSolve[(1-x^2)*D[y[x],{x,2}]-2*x*D[y[x],x]+30*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{8} c_1 x \left (63 x^4-70 x^2+15\right )+c_2 \left (-\frac {63 x^4}{8}+\frac {49 x^2}{8}-\frac {1}{16} \left (63 x^4-70 x^2+15\right ) x (\log (1-x)-\log (x+1))-\frac {8}{15}\right ) \]