4.10.10 \(\left (x^2-y(x)\right ) y'(x)+x=0\)

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 = 0.0171213 (sec), leaf count = 29

\[\left \{\left \{y(x)\to \frac {1}{2} \left (W\left (-e^{c_1-2 x^2-1}\right )+1\right )+x^2\right \}\right \}\]

Maple
cpu = 0.014 (sec), leaf count = 23

\[ \left \{ {\frac { \left (2\,{x}^{2}-2\,y \relax (x ) +1 \right ) {{\rm e}^{2\,y \relax (x ) }}}{2}}+{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

1/2*(2*x^2-2*y(x)+1)*exp(2*y(x))+_C1 = 0