Solve the following initial value problem: 2(y + 3) - xy(dy/dx) = 0, y(1) = -2

Question

Solve the following initial value problem:

2(y + 3) - xy\(\frac{\text{dy}}{\text{dx}}=0, y(1)=-2\)

Answer 1

Given:  2(y + 3) - xy\(\frac{\text{dy}}{\text{dx}}=0\)

Find: Find the particular solution of this differential equation.

Integrating both sides,

Put x = 1 and y= -2 in equation (i), we get

= 2 log(1) = y + 3 – 3 log(-2 + 3) + C

= 0 = 1 - 0 + C

= C = -1

Put the value of C in equation (i), we get