Q14 of 118 Page 395

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


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


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