ODE
\[ (x-2 y(x)) y'(x)+y(x)+2 x=0 \] ODE Classification
[[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
Book solution method
Exact equation
Mathematica ✓
cpu = 0.175662 (sec), leaf count = 55
\[\left \{\left \{y(x)\to \frac {1}{2} \left (x-\sqrt {5 x^2-4 e^{c_1}}\right )\right \},\left \{y(x)\to \frac {1}{2} \left (x+\sqrt {5 x^2-4 e^{c_1}}\right )\right \}\right \}\]
Maple ✓
cpu = 0.061 (sec), leaf count = 53
\[\left [y \left (x \right ) = \frac {\frac {x \textit {\_C1}}{2}-\frac {\sqrt {5 \textit {\_C1}^{2} x^{2}+4}}{2}}{\textit {\_C1}}, y \left (x \right ) = \frac {\frac {x \textit {\_C1}}{2}+\frac {\sqrt {5 \textit {\_C1}^{2} x^{2}+4}}{2}}{\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[2*x + y[x] + (x - 2*y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x - Sqrt[-4*E^C[1] + 5*x^2])/2}, {y[x] -> (x + Sqrt[-4*E^C[1] + 5*x^2])/2}}
Maple raw input
dsolve((x-2*y(x))*diff(y(x),x)+2*x+y(x) = 0, y(x))
Maple raw output
[y(x) = (1/2*x*_C1-1/2*(5*_C1^2*x^2+4)^(1/2))/_C1, y(x) = (1/2*x*_C1+1/2*(5*_C1^2*x^2+4)^(1/2))/_C1]