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Math Help - differentials

  1. #1
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    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
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  2. #2
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    Differential equation

    Hello gracey
    Quote Originally Posted by gracey View Post
    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
    Quote Originally Posted by gracey View Post
    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 \int(5+a\cos2t)dt? This will give you a formula for x in terms of t. (Don't forget c, the constant of integration.)

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

    Can you do it now?

    Grandad
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    thanks but i'm not sure how to integrate the equation
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  4. #4
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    Integration

    Hello gracey

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

    Grandad
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  5. #5
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    thankyou so much, you are amazing
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