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