ODE
\[ \left (x^2-y(x)\right ) y'(x)+x=0 \] ODE Classification
[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]]
Book solution method
Change of Variable, new independent variable
Mathematica ✓
cpu = 0.170364 (sec), leaf count = 29
\[\left \{\left \{y(x)\to x^2+\frac {1}{2} \left (1+W\left (-e^{-2 x^2-1+c_1}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.035 (sec), leaf count = 23
\[\left [y \left (x \right ) = x^{2}+\frac {\LambertW \left (4 \textit {\_C1} \,{\mathrm e}^{-2 x^{2}-1}\right )}{2}+\frac {1}{2}\right ]\] Mathematica raw input
DSolve[x + (x^2 - y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x^2 + (1 + ProductLog[-E^(-1 - 2*x^2 + C[1])])/2}}
Maple raw input
dsolve((x^2-y(x))*diff(y(x),x)+x = 0, y(x))
Maple raw output
[y(x) = x^2+1/2*LambertW(4*_C1*exp(-2*x^2-1))+1/2]