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Math Help - Is this Diff EQ solution wrong?

  1. #1
    Junior Member
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    Is this Diff EQ solution wrong?

    Hi all,

    Here's the problem:

    t(dx/dt) + x = t^3

    1. dx/dt + x/t = t^2

    2. use (1/t) as an integrating factor: e^(int(1/t)dt) = e^(ln t) = t

    3. d/dt (xt) = t^3

    4. xt = (1/4)t^4 + C

    5. x = (1/4)t^3 + C/t

    My friend got the answer k(t)(1/t) = t^3/4 + C/t

    Did I make a mistake or did he? Or both? Thanks,

    Kim
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
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    Chicago, IL
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    Quote Originally Posted by Kim Nu View Post
    Hi all,

    Here's the problem:

    t(dx/dt) + x = t^3

    1. dx/dt + x/t = t^2

    2. use (1/t) as an integrating factor: e^(int(1/t)dt) = e^(ln t) = t

    3. d/dt (xt) = t^3

    4. xt = (1/4)t^4 + C

    5. x = (1/4)t^3 + C/t

    My friend got the answer k(t)(1/t) = t^3/4 + C/t

    Did I make a mistake or did he? Or both? Thanks,

    Kim
    You are correct. How did your friend get k(t)\cdot{\color{red}\frac{1}{t}}=\frac{t^3}{4}+\f  rac{C}{t}??

    --Chris
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  3. #3
    Newbie
    Joined
    Sep 2008
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    You have got it damn right.Actually instead of asking us you can check it out yourself by differentiating what you have obtained.
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