ODE
\[ \sqrt {y''(x)^2+1} \left (1-y'''(x)\right )=y''(x) y'''(x) \] ODE Classification
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.332968 (sec), leaf count = 48
\[\left \{\left \{y(x)\to \frac {1}{12} \left (x^3+3 c_1 x^2+3 \left (2+c_1{}^2+4 c_3\right ) x-6 (x+c_1) \log (x+c_1)+12 c_2\right )\right \}\right \}\]
Maple ✓
cpu = 1.574 (sec), leaf count = 35
\[\left [y \left (x \right ) = \frac {x^{3}}{12}+\frac {x^{2} \textit {\_C1}}{4}-\frac {\ln \left (x +\textit {\_C1} \right ) \left (x +\textit {\_C1} \right )}{2}+\frac {\textit {\_C1}}{2}+\frac {x}{2}+\textit {\_C2} x +\textit {\_C3}\right ]\] Mathematica raw input
DSolve[Sqrt[1 + y''[x]^2]*(1 - y'''[x]) == y''[x]*y'''[x],y[x],x]
Mathematica raw output
{{y[x] -> (x^3 + 3*x^2*C[1] + 12*C[2] + 3*x*(2 + C[1]^2 + 4*C[3]) - 6*(x + C[1])*Log[x + C[1]])/12}}
Maple raw input
dsolve((1-diff(diff(diff(y(x),x),x),x))*(1+diff(diff(y(x),x),x)^2)^(1/2) = diff(diff(y(x),x),x)*diff(diff(diff(y(x),x),x),x), y(x))
Maple raw output
[y(x) = 1/12*x^3+1/4*x^2*_C1-1/2*ln(x+_C1)*(x+_C1)+1/2*_C1+1/2*x+_C2*x+_C3]