4.15.1 $x(2y(x{)}^3+y(x)+x)y^{\prime }(x)=(x-y(x))y(x)$

ODE
$$x(2y(x{)}^3+y(x)+x)y^{\prime }(x)=(x-y(x))y(x)$$ ODE Classification

[_rational]

Book solution method
Exact equation, integrating factor

Mathematica ✓
cpu = 0.504613 (sec), leaf count = 23

$$\text{Solve}[c_1+\frac{x}{y(x)}=y(x{)}^2+\log (y(x))+\log (x),y(x)]$$

Maple ✓
cpu = 0.092 (sec), leaf count = 26

$$\{-\ln \left(x\right)+\frac{x}{y\left(x\right)}-{\left(y\left(x\right)\right)}^2-\ln \left(y\left(x\right)\right)+\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

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

Mathematica raw output

Solve[C[1] + x/y[x] == Log[x] + Log[y[x]] + y[x]^2, y[x]]

Maple raw input

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

Maple raw output

-ln(x)+x/y(x)-y(x)^2-ln(y(x))+_C1 = 0