How Do You Solve the Differential Equation dx/dt = cos(x + t)?

[niceperson]

Homework Statement

solve the differential eqn: dx/dt=cos(x+t)

Homework Equations

The Attempt at a Solution

x'=cos(x+t)=cosxcost-sinxsint

let z=sinx, dz/dx=cosx

dz/dt=(dz/dx).(dx/dt)=cosx(dx/dt)

however this substitution quickly fails

any ideas?

thanksx

 

[D H]

Try something simpler. Hint: You don't need to expand cos(x+t).

 

[niceperson]

Used z=x+t

get: int(1/(cosz+1)=in(t) on separation of the variables.

cheers

 

[D H]

Can you finish the problem now?