ODE
\[ y''(x)^3=12 y'(x) \left (x y''(x)-2 y'(x)\right ) \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✗
cpu = 604.874 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 15.168 (sec), leaf count = 169
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{4}}{9}}+{\it \_C1},y \left ( x \right ) =\int \!{\it RootOf} \left ( -6\,\ln \left ( x \right ) +\int ^{{\it \_Z}}\!-{\frac {1}{{\it \_f}\, \left ( 9\,{\it \_f}-4 \right ) } \left ( 3\,\sqrt {{\frac {1}{{\it \_f}\, \left ( 9\,{\it \_f}-4 \right ) }}}{\it \_f}\,\sqrt [3]{2}\sqrt [3]{ \left ( 3\,\sqrt {{\frac {1}{{\it \_f}\, \left ( 9\,{\it \_f}-4 \right ) }}}{\it \_f}+1 \right ) ^{2} \left ( 9\,{\it \_f}-4 \right ) ^{4}}-2\,{2}^{2/3}\sqrt [3]{ \left ( 3\,\sqrt {{\frac {1}{{\it \_f}\, \left ( 9\,{\it \_f}-4 \right ) }}}{\it \_f}+1 \right ) \left ( 9\,{\it \_f}-4 \right ) ^{2}}-\sqrt [3]{2}\sqrt [3]{ \left ( 3\,\sqrt {{\frac {1}{{\it \_f}\, \left ( 9\,{\it \_f}-4 \right ) }}}{\it \_f}+1 \right ) ^{2} \left ( 9\,{\it \_f}-4 \right ) ^{4}}+18\,{\it \_f}-8 \right ) }{d{\it \_f}}+6\,{\it \_C1} \right ) {x}^{3}\,{\rm d}x+{\it \_C2} \right \} \] Mathematica raw input
DSolve[y''[x]^3 == 12*y'[x]*(-2*y'[x] + x*y''[x]),y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(diff(diff(y(x),x),x)^3 = 12*diff(y(x),x)*(x*diff(diff(y(x),x),x)-2*diff(y(x),x)), y(x),'implicit')
Maple raw output
y(x) = 1/9*x^4+_C1, y(x) = Int(RootOf(-6*ln(x)+Intat(-(3*(1/_f/(9*_f-4))^(1/2)*_f*2^(1/3)*((3*(1/_f/(9*_f-4))^(1/2)*_f+1)^2*(9*_f-4)^4)^(1/3)-2*2^(2/3)*((3*(1/_f/(9*_f-4))^(1/2)*_f+1)*(9*_f-4)^2)^(1/3)-2^(1/3)*((3*(1/_f/(9*_f-4))^(1/2)*_f+1)^2*(9*_f-4)^4)^(1/3)+18*_f-8)/_f/(9*_f-4),_f = _Z)+6*_C1)*x^3,x)+_C2