ODE No. 346

\[ x y'(x) (-a x+y(x)+y(x) \log (x y(x)))-y(x) (a x \log (x y(x))+a x-y(x))=0 \]

✓ Mathematica : cpu = 0.554743 (sec), leaf count = 24

DSolve[-((a*x + a*x*Log[x*y[x]] - y[x])*y[x]) + x*(-(a*x) + y[x] + Log[x*y[x]]*y[x])*Derivative[1][y][x] == 0,y[x],x]

\[\text {Solve}[a x \log (x y(x))-y(x) \log (x y(x))=c_1,y(x)]\]

✓ Maple : cpu = 0.2 (sec), leaf count = 19

dsolve(x*(y(x)*ln(x*y(x))+y(x)-a*x)*diff(y(x),x)-y(x)*(a*x*ln(x*y(x))-y(x)+a*x) = 0,y(x))

\[\left (x y \left (x \right )\right )^{-a x +y \left (x \right )}-c_{1} = 0\]