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 = 0.0539772 (sec), leaf count = 23
\[\left \{\left \{y(x)\to \frac {c_2 \sqrt {c_1+x^5}}{\sqrt {x}}\right \}\right \}\]
Maple ✓
cpu = 0.036 (sec), leaf count = 18
\[ \left \{ -{\it \_C1}\,{x}^{5}-{\frac {5\,x \left ( y \left ( x \right ) \right ) ^{2}}{2}}+{\it \_C2}=0 \right \} \] 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),'implicit')
Maple raw output
-_C1*x^5-5/2*x*y(x)^2+_C2 = 0