4.15.1 \(x \left (2 y(x)^3+y(x)+x\right ) y'(x)=(x-y(x)) y(x)\)

ODE
\[ x \left (2 y(x)^3+y(x)+x\right ) y'(x)=(x-y(x)) y(x) \] ODE Classification

[_rational]

Book solution method
Exact equation, integrating factor

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

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

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

\[ \left \{ -\ln \relax (x ) +{\frac {x}{y \relax (x ) }}- \left (y \relax (x ) \right ) ^{2}-\ln \left (y \relax (x ) \right ) +{\it \_C1}=0 \right \} \] 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