Verify that the given function satisfies the differential equation y=xlogx-x, y=logx

y = (x logx) - x

y = x (logx -1)

take derivation oin both sides

then dy/dx = (logx-1) + (x (1/x))        since d/dx (uv) = d/dx(u)*v - d/dx (v) * u

so dy/dx = logx -1+1

y'' = logx 

                          if you like my answer approve me.                              ------ keep smile -----