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 = 0.411406 (sec), leaf count = 16
\[\text {Solve}\left [\tan ^{-1}\left (\frac {x}{y(x)}\right )+c_1=y(x),y(x)\right ]\]
Maple ✓
cpu = 0.072 (sec), leaf count = 30
\[\left [\textit {\_C1} +\frac {{\mathrm e}^{-2 i y \left (x \right )} \left (i x +y \left (x \right )\right )}{2 i y \left (x \right )+2 x} = 0\right ]\] 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))
Maple raw output
[_C1+exp(-2*I*y(x))*(I*x+y(x))/(2*I*y(x)+2*x) = 0]