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 = 0.115346 (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 = 0.018 (sec), leaf count = 66
\[ \left \{ y \left ( x \right ) = \left ( \left ( -{\frac {2\,\ln \left ( -1+x \right ) }{9}}+{\frac {\ln \left ( {x}^{2}+x+1 \right ) }{9}}+{\frac {2\,\sqrt {3}}{9}\arctan \left ( {\frac { \left ( 1+2\,x \right ) \sqrt {3}}{3}} \right ) }-{\frac {1}{-9+9\,x}}+{\frac {-1+x}{9\,{x}^{2}+9\,x+9}} \right ) {\it \_C1}+{\it \_C2} \right ) \left ( {x}^{3}-1 \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = ((-2/9*ln(-1+x)+1/9*ln(x^2+x+1)+2/9*3^(1/2)*arctan(1/3*(1+2*x)*3^(1/2))-1/9/(-1+x)+1/9*(-1+x)/(x^2+x+1))*_C1+_C2)*(x^3-1)