ODE
\[ \left (x^2+y(x)^2+x\right ) y'(x)=y(x) \] ODE Classification
[_rational]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.0252563 (sec), leaf count = 16
\[\text {Solve}\left [c_1+\tan ^{-1}\left (\frac {x}{y(x)}\right )=y(x),y(x)\right ]\]
Maple ✓
cpu = 0.046 (sec), leaf count = 31
\[ \left \{ {\it \_C1}-{\frac {{{\rm e}^{-2\,iy \left ( x \right ) }} \left ( ix+y \left ( x \right ) \right ) }{2\,iy \left ( x \right ) +2\,x}}=0 \right \} \] Mathematica raw input
DSolve[(x + x^2 + y[x]^2)*y'[x] == y[x],y[x],x]
Mathematica raw output
Solve[ArcTan[x/y[x]] + C[1] == y[x], y[x]]
Maple raw input
dsolve((x+x^2+y(x)^2)*diff(y(x),x) = y(x), y(x),'implicit')
Maple raw output
_C1-exp(-2*I*y(x))*(I*x+y(x))/(2*I*y(x)+2*x) = 0