ODE
\[ \left (1-x^2\right ) \left (y'''(x)\right )^2+2 x y''(x) y'''(x)-y''(x)^2+1=0 \] ODE Classification
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 602.145 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.202 (sec), leaf count = 97
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{3}}{6}\sqrt {{{\it \_C1}}^{2}-1}}+{\frac {{\it \_C1}\,{x}^{2}}{2}}+{\it \_C2}\,x+{\it \_C3},y \left ( x \right ) =-{\frac {1}{6} \left ( -{x}^{2}+1 \right ) ^{{\frac {3}{2}}}}+{\frac {x\arcsin \left ( x \right ) }{2}}+{\frac {1}{2}\sqrt {-{x}^{2}+1}}+{\it \_C1}\,x+{\it \_C2},y \left ( x \right ) ={\frac {1}{6} \left ( -{x}^{2}+1 \right ) ^{{\frac {3}{2}}}}-{\frac {x\arcsin \left ( x \right ) }{2}}-{\frac {1}{2}\sqrt {-{x}^{2}+1}}+{\it \_C1}\,x+{\it \_C2} \right \} \] Mathematica raw input
DSolve[1 - y''[x]^2 + 2*x*y''[x]*y'''[x] + (1 - x^2)*y'''[x]^2 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve((-x^2+1)*diff(diff(diff(y(x),x),x),x)^2+2*x*diff(diff(y(x),x),x)*diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x)^2+1 = 0, y(x),'implicit')
Maple raw output
y(x) = -1/6*(-x^2+1)^(3/2)+1/2*x*arcsin(x)+1/2*(-x^2+1)^(1/2)+_C1*x+_C2, y(x) = 1/6*(-x^2+1)^(3/2)-1/2*x*arcsin(x)-1/2*(-x^2+1)^(1/2)+_C1*x+_C2, y(x) = 1/6*(_C1^2-1)^(1/2)*x^3+1/2*_C1*x^2+_C2*x+_C3