Question

For the differential equation find a particular solution satisfying the given condition:

`cos (dx/dy) = a(a in R); y = 1` when x = 0

Answer 1

`dy/dx = cos^-1 a => dy = (cos^-1"a")` dx

On integrating

`int dy = int (cos^-1 a) dx`

`y = x  cos^-1 a + C`

In this equation y = 1 if x = 0 is put in,

1 = 0 + C ⇒ C = 1

Putting this value of C in equation (i)

`y = x  cos^-1 a + 1`

`(y - 1)/x = cos^-1 a`

`=> cos  (y - 1)/x = a`