4.13.9 $(x^2+y(x{)}^2+x)y^{\prime }(x)=y(x)$

ODE
$$(x^2+y(x{)}^2+x)y^{\prime }(x)=y(x)$$ ODE Classification

[_rational]

Book solution method
Exact equation, integrating factor

Mathematica ✓
cpu = 0.0252563 (sec), leaf count = 16

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

Maple ✓
cpu = 0.046 (sec), leaf count = 31

$$\{\mathit{\_}\mathit{C}\mathit{1}-\frac{{\mathrm{e}}^{-2iy\left(x\right)}(ix+y\left(x\right))}{2iy\left(x\right)+2x}=0\}$$ 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