First order differential equations ? x(dy/dx) -y =2x

Find the solution of
x(dy/dx) -y =2x
answer given is y=2x ln x +cx
thanks in advance

x(dy/dx) - y = 2x

=> Divide by x both sides
=> dy/dx - y/x = 2

Let y/x = v
=> y = vx
=> dy/dx = v + x dv/dx

So, v + x dv/dx - v = 2
=> x dv/dx = 2
=> dx / x = dv / 2
=> ln x = v / 2 + C
=> ln x = y / 2x + C
=> 2x ln x = y + 2Cx
=> y = 2x lnx + Cx
=================

I will describe integral sign as }since i donno where it is
Dy/dx-y/x=2
This is a first degree equation with non variable factors
In general,this form of the equations(y'=dy/dx) are solved this way
Assume y'+a(x)y=b(x)
a(x),b(x) are functions
M(x,y) is a function that when multiplied,the equation is separable by the parameters y and x so that they can be integrated individually on each side of the equation ,leaving y alone on one side of the equation
M(x)=e^}a(x)dx,a(x)=-1/x
M(x)=e^}-1/xdx=e^ln1/x=1/x
Y=1/M(x)[ }M(X) b(x)dx+c]
y=x[ } 2/xdx+c]
Y=x[2lnx+c]
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