1. ## differentials

A point moves on the x -axis so that its coordinate at time t satisfies the differential equation dx/dt = 5 + acos2t for some value of a. it is observed that x=3 when t=0 and x=0 when t=1/4π. Find the value of a and the value of x when t=1/3π.

i am so stuck any help would be much appreciated thanks

2. ## Differential equation

Hello gracey
Originally Posted by gracey
A point moves on the x -axis so that its coordinate at time t satisfies the differential equation dx/dt = 5 + acos2t for some value of a. it is observed that x=3 when t=0 and x=0 when t=1/4
Originally Posted by gracey
π. Find the value of a and the value of x when t=1/3π.

i am so stuck any help would be much appreciated thanks
Do you know how to work out $\displaystyle \int(5+a\cos2t)dt$? This will give you a formula for $\displaystyle x$ in terms of $\displaystyle t$. (Don't forget $\displaystyle c$, the constant of integration.)

Then plug in your two pairs of values of $\displaystyle x$ and $\displaystyle t$, to work out the values of $\displaystyle a$ and $\displaystyle c$. Then you can find $\displaystyle x$ when $\displaystyle t = \tfrac{1}{3}\pi$.

Can you do it now?

3. thanks but i'm not sure how to integrate the equation

4. ## Integration

Hello gracey

$\displaystyle \int(5+a\cos 2t)dt = 5t -\tfrac{1}{2}a\sin 2t + c$