ODE
\[ x^2 y(x) y''(x)+\left (x y'(x)-y(x)\right )^2=3 y(x)^2 \] ODE Classification
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.334009 (sec), leaf count = 23
\[\left \{\left \{y(x)\to \frac {c_2 \sqrt {x^5+c_1}}{\sqrt {x}}\right \}\right \}\]
Maple ✓
cpu = 0.202 (sec), leaf count = 45
\[\left [y \left (x \right ) = -\frac {\sqrt {-10 x \left (\textit {\_C1} \,x^{5}-\textit {\_C2} \right )}}{5 x}, y \left (x \right ) = \frac {\sqrt {-10 x \left (\textit {\_C1} \,x^{5}-\textit {\_C2} \right )}}{5 x}\right ]\] Mathematica raw input
DSolve[(-y[x] + x*y'[x])^2 + x^2*y[x]*y''[x] == 3*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (Sqrt[x^5 + C[1]]*C[2])/Sqrt[x]}}
Maple raw input
dsolve(x^2*y(x)*diff(diff(y(x),x),x)+(x*diff(y(x),x)-y(x))^2 = 3*y(x)^2, y(x))
Maple raw output
[y(x) = -1/5/x*(-10*x*(_C1*x^5-_C2))^(1/2), y(x) = 1/5/x*(-10*x*(_C1*x^5-_C2))^(1/2)]