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


14
1