4.13.9 \(\left (x^2+y(x)^2+x\right ) y'(x)=y(x)\)

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

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