ODE
\[ 2 x y(x) y''(x)=x y'(x)^2-y(x) y'(x) \] ODE Classification
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.319832 (sec), leaf count = 18
\[\left \{\left \{y(x)\to c_2 \left (\sqrt {x}+c_1\right ){}^2\right \}\right \}\]
Maple ✓
cpu = 0.929 (sec), leaf count = 21
\[\left [y \left (x \right ) = \textit {\_C1} \sqrt {x}\, \textit {\_C2} +\textit {\_C1}^{2} x +\frac {\textit {\_C2}^{2}}{4}\right ]\] Mathematica raw input
DSolve[2*x*y[x]*y''[x] == -(y[x]*y'[x]) + x*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (Sqrt[x] + C[1])^2*C[2]}}
Maple raw input
dsolve(2*x*y(x)*diff(diff(y(x),x),x) = x*diff(y(x),x)^2-y(x)*diff(y(x),x), y(x))
Maple raw output
[y(x) = _C1*x^(1/2)*_C2+_C1^2*x+1/4*_C2^2]