ODE
\[ \left (x y''(x)-y'(x)\right )^2=y''(x)^2+1 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✗
cpu = 604.432 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.173 (sec), leaf count = 63
\[ \left \{ y \left ( x \right ) =-{\frac {x}{2}\sqrt {-{x}^{2}+1}}-{\frac {\arcsin \left ( x \right ) }{2}}+{\it \_C1},y \left ( x \right ) ={\frac {x}{2}\sqrt {-{x}^{2}+1}}+{\frac {\arcsin \left ( x \right ) }{2}}+{\it \_C1},y \left ( x \right ) ={\frac {{x}^{2}}{2}\sqrt {{{\it \_C1}}^{2}-1}}+{\it \_C1}\,x+{\it \_C2} \right \} \] Mathematica raw input
DSolve[(-y'[x] + x*y''[x])^2 == 1 + y''[x]^2,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve((x*diff(diff(y(x),x),x)-diff(y(x),x))^2 = 1+diff(diff(y(x),x),x)^2, y(x),'implicit')
Maple raw output
y(x) = 1/2*x*(-x^2+1)^(1/2)+1/2*arcsin(x)+_C1, y(x) = -1/2*x*(-x^2+1)^(1/2)-1/2*arcsin(x)+_C1, y(x) = 1/2*(_C1^2-1)^(1/2)*x^2+_C1*x+_C2