Arbitrary Constant Elimination

Question

Show that y(sec x - tan x) = sec x - tan x + x + k is a general solution for the DE dy/dx + y sec x = tan x

Answer 1

Let prove by getting from general solution given equation. We differentiate left and right side of general solution:

y'(secx - tanx) + y(secxtanx -sec²x) = secxtanx - sec²x + 1, or

y'(secx - tanx) - ysecx(secx - tanx) = tanx(secx - tanx), reducing by secx - tanx we get

y' - ysecx = tanx. This is original equation ( I think mistake in condition)