ODE
\[ 32 y''(x) \left (x y''(x)-y'(x)\right )^3+\left (2 y(x) y''(x)-y'(x)^2\right )^3=0 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.233553 (sec), leaf count = 131
\[\left \{\left \{y(x)\to \frac {1}{4} \left (-\frac {8 c_1{}^3}{\sqrt [3]{3 \sqrt {3} \sqrt {c_1{}^9 c_2{}^9 (-64+27 c_1 c_2)}-27 c_1{}^5 c_2{}^5}}+\frac {c_1{}^2}{c_2}-\frac {2 \sqrt [3]{\sqrt {3} \sqrt {c_1{}^9 c_2{}^9 (-64+27 c_1 c_2)}-9 c_1{}^5 c_2{}^5}}{3^{2/3} c_2{}^3}\right ) x^2+c_1 x+c_2\right \}\right \}\]
Maple ✗
cpu = 0. (sec), leaf count = 0 , hanged
dsolve((2*y(x)*diff(diff(y(x),x),x)-diff(y(x),x)^2)^3+32*diff(diff(y(x),x),x)*(x*diff(diff(y(x),x),x)-diff(y(x),x))^3 = 0, y(x))
Mathematica raw input
DSolve[32*y''[x]*(-y'[x] + x*y''[x])^3 + (-y'[x]^2 + 2*y[x]*y''[x])^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] + C[2] + (x^2*(C[1]^2/C[2] - (2*(-9*C[1]^5*C[2]^5 + Sqrt[3]*Sqrt[C[1]^9*C[2]^9*(-64 + 27*C[1]*C[2])])^(1/3))/(3^(2/3)*C[2]^3) - (8*C[1]^3)/(-27*C[1]^5*C[2]^5 + 3*Sqrt[3]*Sqrt[C[1]^9*C[2]^9*(-64 + 27*C[1]*C[2])])^(1/3)))/4}}
Maple raw input
dsolve((2*y(x)*diff(diff(y(x),x),x)-diff(y(x),x)^2)^3+32*diff(diff(y(x),x),x)*(x*diff(diff(y(x),x),x)-diff(y(x),x))^3 = 0, y(x))
Maple raw output
dsolve((2*y(x)*diff(diff(y(x),x),x)-diff(y(x),x)^2)^3+32*diff(diff(y(x),x),x)*(x*diff(diff(y(x),x),x)-diff(y(x),x))^3 = 0, y(x))