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 = 0.0444144 (sec), leaf count = 48
\[\left \{\left \{y(x)\to \frac {1}{12} \left (3 c_1 x^2+3 \left (c_1^2+4 c_3+2\right ) x-6 \left (c_1+x\right ) \log \left (c_1+x\right )+12 c_2+x^3\right )\right \}\right \}\]
Maple ✓
cpu = 0.202 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) ={\frac { \left ( -6\,x-6\,{\it \_C1} \right ) \ln \left ( {\it \_C1}+x \right ) }{12}}+{\frac {{x}^{3}}{12}}+{\frac {{\it \_C1}\,{x}^{2}}{4}}+{\frac { \left ( 12\,{\it \_C2}+6 \right ) x}{12}}+{\frac {{\it \_C1}}{2}}+{\it \_C3} \right \} \] 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),'implicit')
Maple raw output
y(x) = 1/12*(-6*x-6*_C1)*ln(_C1+x)+1/12*x^3+1/4*_C1*x^2+1/12*(12*_C2+6)*x+1/2*_C1+_C3