How to estimate the behavior of a solution of a differential equation at \infty?

[wdlang]

i have a first order nonlinear differential equation

y'=-sin^2(kx+y)/kx

the boundary condition is y(x=0)=0

here k is a real positive number

i want to estimate the behavior of y as x goes to infinity

how to do this?

any book for reference?

 

[Eynstone]

As sin^2(kx+y) is bounded , sin^2(kx+y)/kx -> 0 as x->infinity. Therefore, y will tend to a constant as x->infinity , regardless of the initial condition .