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 = 0.647796 (sec), leaf count = 23
\[\text {Solve}\left [\frac {x}{y(x)}+c_1=y(x)^2+\log (y(x))+\log (x),y(x)\right ]\]
Maple ✓
cpu = 0.221 (sec), leaf count = 29
\[[y \left (x \right ) = {\mathrm e}^{\RootOf \left (-{\mathrm e}^{3 \textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} \ln \left (x \right )+{\mathrm e}^{\textit {\_Z}} \textit {\_C1} -{\mathrm e}^{\textit {\_Z}} \textit {\_Z} +x \right )}]\] 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))
Maple raw output
[y(x) = exp(RootOf(-exp(_Z)^3-exp(_Z)*ln(x)+exp(_Z)*_C1-exp(_Z)*_Z+x))]