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Math Help - O.D.E Help

  1. #1
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    O.D.E Help

    Hey, first time post, I found this place by Googling "Math Help Forum". Sorry for not knowing the script to write out math eqn's, so here goes.

    I'm trying to figure out the following ODE:

    y' - 6tan(3x)*y + 2cos(5x) = 0

    I'm 99% sure it's a Linear ODE so I rewrote it as:

    y' - 6tan(3x)*y = -2cos(5x)

    Found an integrating factor mu = e^(2ln(cos(3x)) = (cos(3x))^2

    However this does not leave me the result of a product rule.

    y'*(cos(3x))^2 - 6sin(3x)*cos(3x)*y = (-2cos(5x))^3

    I tried dividing by cos(3x) which gave me

    cos(3x)*y' - 6sin(3x)*y = (-2cos(5x))^2

    Which looks like it should be the result of a product derivative, however at this point I know something is wrong, as either I need to have 2cos(3x) or -3sin(3x) for things to work out. Where am I going wrong?
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  2. #2
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    Quote Originally Posted by BigC View Post
    Hey, first time post, I found this place by Googling "Math Help Forum". Sorry for not knowing the script to write out math eqn's, so here goes.

    I'm trying to figure out the following ODE:

    y' - 6tan(3x)*y + 2cos(5x) = 0

    I'm 99% sure it's a Linear ODE so I rewrote it as:

    y' - 6tan(3x)*y = -2cos(5x)

    Found an integrating factor mu = e^(2ln(cos(3x)) = (cos(3x))^2 Mr F says: Correct.

    However this does not leave me the result of a product rule. Mr F says: Yes it does (see main reply).

    y'*(cos(3x))^2 - 6sin(3x)*cos(3x)*y = (-2cos(5x))^3

    I tried dividing by cos(3x) which gave me

    cos(3x)*y' - 6sin(3x)*y = (-2cos(5x))^2

    Which looks like it should be the result of a product derivative, however at this point I know something is wrong, as either I need to have 2cos(3x) or -3sin(3x) for things to work out. Where am I going wrong?
    \frac{d}{dx} \left[ y \cos^2 (3x)\right] = \cos^2 (3x) \frac{dy}{dx} - 6 \sin (3x) \cos (3x) y.

    So there's no trouble here. Go ahead and continue the process.
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  3. #3
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    I guess I just need to practice and re-memorize my rules of differentiation. I didn't even remember the derivative of cos(x)^2
    Thanks for the help
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