4.9.49 \((y(x)+2 x) y'(x)-2 y(x)+x=0\)

ODE
\[ (y(x)+2 x) y'(x)-2 y(x)+x=0 \] ODE Classification

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type``class A`]]

Book solution method
Homogeneous equation

Mathematica
cpu = 0.0310198 (sec), leaf count = 33

\[\text {Solve}\left [\log \left (\frac {y(x)^2}{x^2}+1\right )+4 \tan ^{-1}\left (\frac {y(x)}{x}\right )+2 \log (x)=2 c_1,y(x)\right ]\]

Maple
cpu = 0.012 (sec), leaf count = 35

\[ \left \{ -{\frac {1}{2}\ln \left ({\frac {{x}^{2}+ \left (y \relax (x ) \right ) ^{2}}{{x}^{2}}} \right ) }-2\,\arctan \left ({\frac {y \relax (x ) }{x}} \right ) -\ln \relax (x ) -{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[x - 2*y[x] + (2*x + y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

Solve[4*ArcTan[y[x]/x] + 2*Log[x] + Log[1 + y[x]^2/x^2] == 2*C[1], y[x]]

Maple raw input

dsolve((2*x+y(x))*diff(y(x),x)+x-2*y(x) = 0, y(x),'implicit')

Maple raw output

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