# First-order differential equation

Mathematicsss

y'+tanxy=sinx

## Homework Equations

integrating factor I(x)= exp{lnIsecxI}[/B]

## The Attempt at a Solution

I have secxy= integral of sinx I(x)
I am not sure how to integrate that because secx is in absolute value form.[/B]

Ray Vickson
Homework Helper
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y'+tanxy=sinx

## Homework Equations

integrating factor I(x)= exp{lnIsecxI}[/B]

## The Attempt at a Solution

I have secxy= integral of sinx I(x)
I am not sure how to integrate that because secx is in absolute value form.[/B]

There are two cases: (1) the values of ##x## make ##\sec(x) > 0##; or (2) the values of ##x## make ##\sec(x) < 0##. Just analyze both cases, although you need to worry about whether the solution ##y(x)## can remain meaningful if ##x## crosses from one region to the other.