"Verify that the given differential equation is exact; then solve it."
(e^(x) * siny + tany)dx + (e^(x) * cosy + x * (secy)^2)dy = 0
To be exact, the term in front of dx must be
and the term in front of dy must be , WHERE the bottom line is to find that .
Ignore the silly N and M in must books, it's foolish.
Next from Clarabell's theorem
and in our case that's correct, we get in both cases.
So, it's exact. Hence integrate the wrt x
and wrt y to get this and when you integrate, don't just add +C
in the first case it's and the second it's .
You mean
when you have more than one symbol after _ or ^, you need { } around them.
and in our case that's correct, we get in both cases.
So, it's exact. Hence integrate the wrt x
and wrt y to get this and when you integratse, don't just add +C
in the first case it's and the second it's .