# Trigonometric First Order DE

$$\frac{dx}{dt} = \cos(x+t)$$

I'm having real troubles with this; I tried a substitution of $$u=x+t$$ but it just ends up as,

$$t=\tan{u} + \csc{u} + C$$

And I can't see where to go from there. (the middle function is cosec; it didn't come out very clearly on my screen).

Dick
Homework Helper
I keep getting t=csc(u)-cot(u)+C. You could then put u=x+t. But I don't think you can go much further than that as far as explicitly solving for x(t). It looks like kind of a mess.

You're right, it is -cot(u) rather than tan(u); don't know where I got that from. But you don't believe there's anyway to get it into a form x(t) [or even t(x)]?

Last edited:
Dick