ODE
\[ y^{(n-2)}(x) y^{(n)}(x)=y^{(n-1)}(x)^2 \] ODE Classification
(ODEtools/info) missing specification of intermediate function
Book solution method
TO DO
Mathematica ✗
cpu = 0.00511658 (sec), leaf count = 0 , could not solve
DSolve[Derivative[-2 + n][y][x]*Derivative[n][y][x] == Derivative[-1 + n][y][x]^2, y[x], x]
Maple ✗
cpu = 0.479 (sec), leaf count = 0 , exception
unable to handle ODEs of undefined differential order
Mathematica raw input
DSolve[Derivative[-2 + n][y][x]*Derivative[n][y][x] == Derivative[-1 + n][y][x]^2,y[x],x]
Mathematica raw output
DSolve[Derivative[-2 + n][y][x]*Derivative[n][y][x] == Derivative[-1 + n][y][x]^2, y[x], x]
Maple raw input
dsolve(diff(y(x),[`$`(x,n-2)])*diff(y(x),[`$`(x,n)]) = diff(y(x),[`$`(x,n-1)])^2, y(x),'implicit')
Maple raw output
unable to handle ODEs of undefined differential order