Solve the following initial value problem: xy(dy/dx) = y + 2, y(2) = 0

Question

Solve the following initial value problem:

xy\(\frac{\text{dy}}{\text{dx}}=\) y + 2, y(2) = 0

Answer 1

Given differential equation xy\(\frac{\text{dy}}{\text{dx}}=\) y + 2

Find: Find the general solution of this differential equation.

On Integrating we get,

= y – 2 log |y + 2| = log |x| + log |C| ….(i)

Put y = 0, x = 2

= 0 – 2 log 2 = log 2 + log c

= -2 log 2 – log 2 = log C

= -3 log 2 = log c

Put the value of C in equation (i)

Hence, y – 2 log |y + 2| = log \(\left|\frac{\text{x}}{8}\right|\)