ODE
\[ 2 y'(x) y'''(x)=2 y''(x)^2 \] ODE Classification
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.195402 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \frac {c_2 e^{c_1 x}}{c_1}+c_3\right \}\right \}\]
Maple ✓
cpu = 1.671 (sec), leaf count = 18
\[\left [y \left (x \right ) = \frac {{\mathrm e}^{\textit {\_C2} \textit {\_C1}} {\mathrm e}^{\textit {\_C1} x}}{\textit {\_C1}}+\textit {\_C3}\right ]\] Mathematica raw input
DSolve[2*y'[x]*y'''[x] == 2*y''[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (E^(x*C[1])*C[2])/C[1] + C[3]}}
Maple raw input
dsolve(2*diff(y(x),x)*diff(diff(diff(y(x),x),x),x) = 2*diff(diff(y(x),x),x)^2, y(x))
Maple raw output
[y(x) = 1/_C1*exp(_C2*_C1)*exp(_C1*x)+_C3]