Find the Particular Solution of the Differential Equation $x d y = ( x + y + 6 ) d x \text { that }$

Multiple Choice

Find the particular solution of the differential equation $x d y = ( x + y + 6 ) d x \text { that }$ satisfies the boundary condition $y ( 1 ) = 5$ .

A) $y = 6 x \ln | x | - 10 x - 5$
B) $y = x \ln | x | + 11 x - 6$
C) $y = x \ln | x | + 11 x + 5$
D) $y = 6 x \ln | x | + 10 x - 5$
E) $y = x \ln | x | - 11 x + 6$