4.11.25 \((x (-y(x))+3 x+2) y'(x)+y(x)=0\)

ODE
\[ (x (-y(x))+3 x+2) y'(x)+y(x)=0 \] ODE Classification

[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type``class B`]]

Book solution method
Change of Variable, new independent variable

Mathematica
cpu = 0.0730179 (sec), leaf count = 29

\[\text {Solve}\left [x=\frac {c_1 e^{y(x)}+2 y(x)^2+4 y(x)+4}{y(x)^3},y(x)\right ]\]

Maple
cpu = 0.044 (sec), leaf count = 29

\[ \left \{ {\it \_C1}+{\frac {{{\rm e}^{y \relax (x ) }}}{x \left (y \relax (x ) \right ) ^{3}-2\, \left (y \relax (x ) \right ) ^{2}-4\,y \relax (x ) -4}}=0 \right \} \] Mathematica raw input

DSolve[y[x] + (2 + 3*x - x*y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

Solve[x == (4 + E^y[x]*C[1] + 4*y[x] + 2*y[x]^2)/y[x]^3, y[x]]

Maple raw input

dsolve((2+3*x-x*y(x))*diff(y(x),x)+y(x) = 0, y(x),'implicit')

Maple raw output

_C1+exp(y(x))/(x*y(x)^3-2*y(x)^2-4*y(x)-4) = 0