First-order differential equation

[Mathematicsss]

Homework Statement

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 Statement

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.