ODE
\[ 2 y(x) y''(x)=y'(x)^2 \] ODE Classification
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00837532 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {\left (c_1 x+2 c_2\right ){}^2}{4 c_2}\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 17
\[ \left \{ 2\,\sqrt {y \left ( x \right ) }-{\it \_C1}\,x-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[2*y[x]*y''[x] == y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (x*C[1] + 2*C[2])^2/(4*C[2])}}
Maple raw input
dsolve(2*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2, y(x),'implicit')
Maple raw output
2*y(x)^(1/2)-_C1*x-_C2 = 0