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Math Help - dy/dx=e^(-x^2) - 2xy subject to y(2)=0

  1. #1
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    dy/dx=e^(-x^2) - 2xy subject to y(2)=0

    hi,
    need some help for this question, i tried solving by seperating dy to one side and dx to the other and integrating however dont get the right answer...how can i solve this
    any help much appreciated

    solve the following differential equation for y giving answer in form y=f(x)

    dy/dx=e^(-x^2) - 2xy subject to y(2)=0

    thankyou
    Last edited by mr fantastic; June 3rd 2011 at 02:02 PM. Reason: Re-titled.
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  2. #2
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    The equation is linear in y, so use the integrating factor approach. What do you get?
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  3. #3
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    i used the integrating factor method
    integrating factor being e^(x^2)
    i got the answer to be y=2/(e^(x^2))

    but the answer book shows the answer to be
    y = (x-2)e^(-x^2)


    thankyou for your quick reply
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  4. #4
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    Quote Originally Posted by metalkakkarot View Post
    i used the integrating factor method
    integrating factor being e^(x^2)
    That is correct.

    i got the answer to be y=2/(e^(x^2))

    but the answer book shows the answer to be
    y = (x-2)e^(-x^2)


    thankyou for your quick reply
    The book is correct. How did you get your answer? Can you please show the steps?
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  5. #5
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    sorry for delayed reply had to upload the photo from my mobile..
    i did the question again and essentially had forgotten to integrate the RHS first time round...
    now i get close to the correct answer except a sign difference...
    at the end i subbed y=2 and x=0 to get c=2


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  6. #6
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    Your working is correct up to the determination of the arbitrary constant. If you plug in x = 2, do you get y = 0? (I suspect you may have reversed the roles of x and y, perhaps?)
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  7. #7
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    thankyou so much...it was as you said i had switched the x and the y and the end....got the answer

    +thanks
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  8. #8
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    You're very welcome. Have a good one!
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