Solve the following initial value problem:

Given:

Find: Find the particular solution of this differential equation.

=

=

= y – 2 log|y + 2| = x + 2 log|x| + C

= y – 2 log|y + 2| - x - 2 log|x| = C

Put x =1, y = -1

= -1 -1-2log(-1 + 2) – 2log 1 = C

= -2 = C

Thus, we have

Hence, Y – x – 2log(y + 2) - 2log x = -2