Question

Solve: 2(y + 3) - xy dy/dx = 0, given that y (1) = –2.

Answer 1

Given: 2(y + 3) - xy dy/dx = 0 and (1, -2) is a solution

To find: solution of given differential equation

Re-writing the equation as

Substituting (-2,1) to find the value of c

0=-2+c

c=2

⇒ 2 ln x=y-3 ln (y+3) +2

⇒ 2 ln x +3 ln (y+3) =y+2

⇒ 2 ln x +3 ln (y+3) =y+2

⇒ ln x² + ln (y+3)³ =y+2

⇒ x²(y+3)³ = y + c