ODE
\[ x^2 y(x) y''(x)+\left (x y'(x)-y(x)\right )^2=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.315209 (sec), leaf count = 23
\[\left \{\left \{y(x)\to c_2 \sqrt {x} \sqrt {2 x+c_1}\right \}\right \}\]
Maple ✓
cpu = 0.231 (sec), leaf count = 35
\[\left [y \left (x \right ) = \sqrt {-2 x^{2} \textit {\_C1} +2 \textit {\_C2} x}, y \left (x \right ) = -\sqrt {-2 x^{2} \textit {\_C1} +2 \textit {\_C2} x}\right ]\] Mathematica raw input
DSolve[(-y[x] + x*y'[x])^2 + x^2*y[x]*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> Sqrt[x]*Sqrt[2*x + C[1]]*C[2]}}
Maple raw input
dsolve(x^2*y(x)*diff(diff(y(x),x),x)+(x*diff(y(x),x)-y(x))^2 = 0, y(x))
Maple raw output
[y(x) = (-2*_C1*x^2+2*_C2*x)^(1/2), y(x) = -(-2*_C1*x^2+2*_C2*x)^(1/2)]