Find the particular solutions of the following differential equation :
(1) xdx + ydy =0 , when x =3 , y =4

Explanation

(1) The given differential equation is xdy +ydx =0
Integrating we get,
`int x dx + int ydy =c_(1)`
`x^(2)/2 +y^(2)/2 = c_(1)`
` x^(2)/2 + y^(2)/2 =c_(1)`
` x^(2) +y^(2) =c " where" c= 2c_(1)`
This is the general solution.
When x=3, y=4, we get,
` 3^(2) +4^(2) =c " " therefore c=25`
The particular solution is ` x^(2) +y^(2) =25`