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 = 0.158874 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {(c_1 x+2 c_2){}^2}{4 c_2}\right \}\right \}\]
Maple ✓
cpu = 0.863 (sec), leaf count = 23
\[\left [y \left (x \right ) = \frac {1}{4} \textit {\_C1}^{2} x^{2}+\frac {1}{2} \textit {\_C1} x \textit {\_C2} +\frac {1}{4} \textit {\_C2}^{2}\right ]\] 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))
Maple raw output
[y(x) = 1/4*_C1^2*x^2+1/2*_C1*x*_C2+1/4*_C2^2]