Solve the given differential equation by using an appropriate substitution. The DE is homogeneous. \[ x d x+(y-2 x) d y=0 \]

Step 1 ：Given the homogeneous differential equation \(x dx+(y-2 x) dy=0\)

Step 2 ：We use the substitution \(y=vx\). The derivative of \(y\) with respect to \(x\) (\(dy/dx\)) will then be \(v + x dv/dx\).

Step 3 ：Substitute these into the differential equation and solve for \(v\).

Step 4 ：The solution to the differential equation in terms of \(v\) is \(v(x) = 1 + \exp(C1 + \text{LambertW}(-x*\exp(-C1)))/x\).

Step 5 ：Substitute \(v\) back into \(y = vx\) to get the solution in terms of \(y\).

Step 6 ：\(y = x*(1 + \exp(C1 + \text{LambertW}(-x*\exp(-C1)))/x)\)

Step 7 ：\(\boxed{y = x*(1 + \exp(C1 + \text{LambertW}(-x*\exp(-C1)))/x)}\) is the final solution to the given homogeneous differential equation.