Limit of an explicitly unsolvable differential equation

[spinning-p]

Homework Statement

initial value problem:

x(0)=-6

dx/dt=e^((x^2)/2)sin(5x)

find the limit of x(t) as t approaches infinity.

--I'm really unsure as to how to approach this... I was thinking along the lines of seeing where the derivative equalled zero (since if the rate of change is zero it would be indicative of a limit..) but then because of sin(5x) there are so many possibilities to this and I wasn't sure how to incorporate the initial value.

Any help would be really appreciated! Thanks :)

 

[Dick]

x(t) can only have a limit L if x'(L)=0. That means sin(5L)=0. Which limiting value can you possibly approach? Is it a stable point?