ODE
\[ y'(x) y''(x)=a x y'(x)^5+3 y''(x)^2 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✗
cpu = 7.22642 (sec), leaf count = 0 , could not solve
DSolve[Derivative[1][y][x]*Derivative[2][y][x] == a*x*Derivative[1][y][x]^5 + 3*Derivative[2][y][x]^2, y[x], x]
Maple ✓
cpu = 1.792 (sec), leaf count = 5
\[[y \left (x \right ) = \textit {\_C1}]\] Mathematica raw input
DSolve[y'[x]*y''[x] == a*x*y'[x]^5 + 3*y''[x]^2,y[x],x]
Mathematica raw output
DSolve[Derivative[1][y][x]*Derivative[2][y][x] == a*x*Derivative[1][y][x]^5 + 3*Derivative[2][y][x]^2, y[x], x]
Maple raw input
dsolve(diff(y(x),x)*diff(diff(y(x),x),x) = a*x*diff(y(x),x)^5+3*diff(diff(y(x),x),x)^2, y(x))
Maple raw output
[y(x) = _C1]