ODE
\[ \left (1-x^3\right ) y''(x)+6 x y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.206447 (sec), leaf count = 81
\[\left \{\left \{y(x)\to c_1 \left (x^3-1\right )+\frac {1}{9} c_2 \left (-2 \left (x^3-1\right ) \log (1-x)+2 \sqrt {3} \left (x^3-1\right ) \tan ^{-1}\left (\frac {2 x+1}{\sqrt {3}}\right )-\log \left (x^2+x+1\right )+x^3 \log \left (x^2+x+1\right )-3 x\right )\right \}\right \}\]
Maple ✓
cpu = 0.05 (sec), leaf count = 66
\[\left [y \left (x \right ) = \left (\left (\frac {x -1}{9 x^{2}+9 x +9}+\frac {\ln \left (x^{2}+x +1\right )}{9}+\frac {2 \sqrt {3}\, \arctan \left (\frac {\left (1+2 x \right ) \sqrt {3}}{3}\right )}{9}-\frac {1}{9 \left (x -1\right )}-\frac {2 \ln \left (x -1\right )}{9}\right ) \textit {\_C1} +\textit {\_C2} \right ) \left (x^{3}-1\right )\right ]\] Mathematica raw input
DSolve[6*x*y[x] + (1 - x^3)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-1 + x^3)*C[1] + (C[2]*(-3*x + 2*Sqrt[3]*(-1 + x^3)*ArcTan[(1 + 2*x)/Sqrt[3]] - 2*(-1 + x^3)*Log[1 - x] - Log[1 + x + x^2] + x^3*Log[1 + x + x^2]))/9}}
Maple raw input
dsolve((-x^3+1)*diff(diff(y(x),x),x)+6*x*y(x) = 0, y(x))
Maple raw output
[y(x) = ((1/9*(x-1)/(x^2+x+1)+1/9*ln(x^2+x+1)+2/9*3^(1/2)*arctan(1/3*(1+2*x)*3^(1/2))-1/9/(x-1)-2/9*ln(x-1))*_C1+_C2)*(x^3-1)]