For each of the differential equations in question, find a particular solution satisfying the given condition:

Question

For each of the differential equations in question, find a particular solution satisfying the given condition: dy/dx = y tan x; y = 1 when x = 0

Philoid · Accepted Answer

Separating variables,

Integrating both sides,

⇒ log y = -log (cos x) + log c

Or,

⇒ log y = log (sec x) + log c

⇒ log y = log c (sec x)

⇒ y = c (sec x) -i)

Now we are given that y = 1 when x = 0

⇒ 1 = c (sec 0)

⇒ 1 = c × 1

⇒ c = 1

Putting the value of c in i)

⇒ y = sec x