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Math Help - differential equation verification

  1. #1
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    differential equation verification

    (dy/dt) + y = cos(e^t) i got the integrating factor as e^t and the answer i got is y = (1/(e^t))*(sin (e^t)) + C is this correct???
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  2. #2
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    Quote Originally Posted by crafty View Post
    (dy/dt) + y = cos(e^t) i got the integrating factor as e^t and the answer i got is y = (1/(e^t))*(sin (e^t)) + C is this correct???
    Very close, when you integrate, you get

    e^t y = \sin e^t + c

    Dividing by e^t you must keep the c where it is,

     y = \frac{\sin e^t + c}{e^t} a little different from your answer.
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  3. #3
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    but isnt c just an arbitrary constant and assuming my c outside is a different constant would it still be correct or is there something special about this case, if there is can you explain why ... thanks in advance
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  4. #4
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    Quote Originally Posted by crafty View Post
    but isnt c just an arbitrary constant and assuming my c outside is a different constant would it still be correct or is there something special about this case, if there is can you explain why ... thanks in advance
    Your right c is an arbitrary constant but when multiplied by a function of t then it will change with respect to t (it's no longer fixed). This is really seen if you were given an initial condition were the value of c would be set.
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  5. #5
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    oh right i get it now and can you please reply to my other thread called its called "how do is solve this differential eqn???" ive been waiting a while for that one and i still don't get it
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