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 = 0.315754 (sec), leaf count = 24
\[\left \{\left \{y(x)\to e^{-c_1} c_2 \tan ^{-1}\left (e^{x+c_1}\right )+c_3\right \}\right \}\]
Maple ✓
cpu = 2.641 (sec), leaf count = 48
\[\left [y \left (x \right ) = \ln \left (\tanh \left (\frac {x}{2}+\frac {\textit {\_C3}}{2}\right ) {\mathrm e}^{-\frac {\textit {\_C2}}{\textit {\_C1}}}\right ) \textit {\_C1}, y \left (x \right ) = \ln \left (-\tanh \left (\frac {x}{2}+\frac {\textit {\_C3}}{2}\right ) {\mathrm e}^{-\frac {\textit {\_C2}}{\textit {\_C1}}}\right ) \textit {\_C1}\right ]\] 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))
Maple raw output
[y(x) = ln(tanh(1/2*x+1/2*_C3)/exp(1/_C1*_C2))*_C1, y(x) = ln(-tanh(1/2*x+1/2*_C3)/exp(1/_C1*_C2))*_C1]