ODE
\[ x y(x) y''(x)+x y'(x)^2=y(x) y'(x) \] ODE Classification
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.30387 (sec), leaf count = 18
\[\left \{\left \{y(x)\to c_2 \sqrt {x^2+c_1}\right \}\right \}\]
Maple ✓
cpu = 0.102 (sec), leaf count = 31
\[\left [y \left (x \right ) = \sqrt {x^{2} \textit {\_C1} +2 \textit {\_C2}}, y \left (x \right ) = -\sqrt {x^{2} \textit {\_C1} +2 \textit {\_C2}}\right ]\] Mathematica raw input
DSolve[x*y'[x]^2 + x*y[x]*y''[x] == y[x]*y'[x],y[x],x]
Mathematica raw output
{{y[x] -> Sqrt[x^2 + C[1]]*C[2]}}
Maple raw input
dsolve(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^2+2*_C2)^(1/2), y(x) = -(_C1*x^2+2*_C2)^(1/2)]