Determine wether or not the following equations areis exact

Determine wether or not the following equations are/is exact. If so, find the solution.

((y/x)+6x)dx+(lnx-2)dy=0, y(e)=1

This equation is fo the form

Mdx+Ndy=0

M_y=1/x

N_x=1/x

Subscript denotes partial derivative w.r.t. that variable

M_y=N_x

Hence equation is exact

Integral is
F(x,y)=C

where C is integration constant

so that

dF=Mdx+Ndy=F_xdx+F_ydy=0

So,

F_y=ln x-2

INtegrating. w.r.t. y treating x as a constant gives

F=y ln(x)-2y+g(x)

F_x=y/x+g\'=y/x+6x

So, g\'=6x

g=3x^2

So,

F=y ln(x)-2y+3x^2=C