Question

The solution of the differential equation dy/dx = sec x – y tan x is:

(A) y sec x = tan x + c

(B) y sec x + tan x = c

(C) sec x = y tan x + c

(D) sec x + y tan x = c

Answer 1

(A)

`dy/dx+ytanx=secx`

The given equation is of the form

`dy/dx+Py=Q`

`I.f==e^(intPdx)=e^(inttanxdx)`

`=e^(log|secx|)`

=secx

Solution of the given equation is

`y.( I.F)=intQ(I.F)dx+c`

`ysecx=intsecxsecxdx+c`

ysecx=tanx+c