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 = 27.2555 (sec), leaf count = 0 , could not solve
DSolve[Derivative[2][y][x]^3 == 12*Derivative[1][y][x]*(-2*Derivative[1][y][x] + x*Derivative[2][y][x]), y[x], x]
Maple ✓
cpu = 18.471 (sec), leaf count = 174
\[\left [y \left (x \right ) = \frac {x^{4}}{9}+\textit {\_C1}, y \left (x \right ) = \textit {\_C1}, y \left (x \right ) = \int \RootOf \left (-6 \ln \left (x \right )-\left (\int _{}^{\textit {\_Z}}\frac {3 \textit {\_f} \sqrt {\frac {1}{\textit {\_f} \left (9 \textit {\_f} -4\right )}}\, 2^{\frac {1}{3}} \left (\left (3 \sqrt {\frac {1}{\textit {\_f} \left (9 \textit {\_f} -4\right )}}\, \textit {\_f} +1\right )^{2} \left (9 \textit {\_f} -4\right )^{4}\right )^{\frac {1}{3}}-2 \,2^{\frac {2}{3}} \left (\left (3 \sqrt {\frac {1}{\textit {\_f} \left (9 \textit {\_f} -4\right )}}\, \textit {\_f} +1\right ) \left (9 \textit {\_f} -4\right )^{2}\right )^{\frac {1}{3}}-2^{\frac {1}{3}} \left (\left (3 \sqrt {\frac {1}{\textit {\_f} \left (9 \textit {\_f} -4\right )}}\, \textit {\_f} +1\right )^{2} \left (9 \textit {\_f} -4\right )^{4}\right )^{\frac {1}{3}}+18 \textit {\_f} -8}{\textit {\_f} \left (9 \textit {\_f} -4\right )}d \textit {\_f} \right )+6 \textit {\_C1} \right ) x^{3}d x +\textit {\_C2}\right ]\] Mathematica raw input
DSolve[y''[x]^3 == 12*y'[x]*(-2*y'[x] + x*y''[x]),y[x],x]
Mathematica raw output
DSolve[Derivative[2][y][x]^3 == 12*Derivative[1][y][x]*(-2*Derivative[1][y][x] + x*Derivative[2][y][x]), y[x], x]
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))
Maple raw output
[y(x) = 1/9*x^4+_C1, y(x) = _C1, y(x) = Int(RootOf(-6*ln(x)-Intat((3*_f*(1/_f/(9*_f-4))^(1/2)*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]