ODE
\[ y'(x) y'''(x)+y'(x)^2=2 y''(x)^2 \] ODE Classification
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0936004 (sec), leaf count = 24
\[\left \{\left \{y(x)\to e^{-c_1} c_2 \tan ^{-1}\left (e^{c_1+x}\right )+c_3\right \}\right \}\]
Maple ✓
cpu = 0.453 (sec), leaf count = 53
\[ \left \{ -2\,{\it Artanh} \left ( {{\rm e}^{{\frac {{\it \_C2}}{{\it \_C1}}}}}{{\rm e}^{{\frac {y \left ( x \right ) }{{\it \_C1}}}}} \right ) -x-{\it \_C3}=0,2\,{\it Artanh} \left ( {{\rm e}^{{\frac {{\it \_C2}}{{\it \_C1}}}}}{{\rm e}^{{\frac {y \left ( x \right ) }{{\it \_C1}}}}} \right ) -x-{\it \_C3}=0 \right \} \] Mathematica raw input
DSolve[y'[x]^2 + y'[x]*y'''[x] == 2*y''[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (ArcTan[E^(x + C[1])]*C[2])/E^C[1] + C[3]}}
Maple raw input
dsolve(diff(y(x),x)*diff(diff(diff(y(x),x),x),x)+diff(y(x),x)^2 = 2*diff(diff(y(x),x),x)^2, y(x),'implicit')
Maple raw output
-2*arctanh(exp(1/_C1*_C2)*exp(1/_C1*y(x)))-x-_C3 = 0, 2*arctanh(exp(1/_C1*_C2)*exp(1/_C1*y(x)))-x-_C3 = 0