# The solution of the differential equation dy/dx = sec x – y tan x is: - Mathematics and Statistics

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

#### Solution

(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

Concept: General and Particular Solutions of a Differential Equation
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