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 = 0.0247698 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \frac {c_2 e^{c_1 x}}{c_1}+c_3\right \}\right \}\]
Maple ✓
cpu = 0.114 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{{\it \_C2}\,{\it \_C1}}}{{\rm e}^{{\it \_C1}\,x}}}{{\it \_C1}}}+{\it \_C3} \right \} \] 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),'implicit')
Maple raw output
y(x) = 1/_C1*exp(_C2*_C1)*exp(_C1*x)+_C3