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