✓ Mathematica : cpu = 0.0574562 (sec), leaf count = 17
DSolve[-(y[x]*(-1 + 2*Log[x]*y[x])) + x*Derivative[1][y][x] == 0,y[x],x]
✓ Maple : cpu = 0.013 (sec), leaf count = 15
dsolve(x*diff(y(x),x)-y(x)*(2*y(x)*ln(x)-1) = 0,y(x))
Hand solution
This is Bernoulli non-linear first order ODE since
Putting
Integrating factor is
Integrating
Therefore
Since
Verification
restart; ode:=x*diff(y(x),x)-y(x)*(2*y(x)*ln(x)-1)=0; my_solution:=1/(2*(ln(x)+1)+_C1*x); odetest(y(x)=my_solution,ode); 0