Question

Verify that y sec x = tan x + c is a solution of the differential equation `dy/dx + y tan x` = sec x.

Answer 1

y sec x = tan x + c

Differentiating w.r.t.x, we get

`y*d/dx(secx) + secx*dy/dx` = sec²x + 0

∴ `y*secx tanx + secx*dy/dx` = sec²x

∴ `dy/dx + y tan x` = sec x

Hence, y sec x = tan x + c is a solution of the differential equation `dy/dx + y tan x` = sec x.