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Math Help - Differential equation

  1. #1
    Junior Member ceode's Avatar
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    Differential equation

    1)
    solve

    dy/dx + (y logy)/x = y(logy)^2/(x^2)

    2)
    SOLVE
    (x*y^2)dx - e^(1/(x^3))dx - (x^2)*y dy = 0

    Thank you
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Santa Cruz, CA
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    3
    Quote Originally Posted by ceode View Post
    1)
    solve

    dy/dx + (y logy)/x = y(logy)^2/(x^2)

    2)
    SOLVE
    (x*y^2)dx - e^(1/(x^3))dx - (x^2)*y dy = 0

    Thank you
    For the first one, make the substitution u=\dfrac{\log y}{x} (assume you're letting \log y mean natural log [base e]). It will then become a simple separable equation.

    For the second one, rewrite it as \dfrac{dy}{dx}-\dfrac{1}{x}y=-\dfrac{1}{x^2}e^{-1/x^3}y^{-1}; this is a Bernoulli equation.

    Can you take it from here?
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  3. #3
    Junior Member ceode's Avatar
    Joined
    Sep 2010
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    india
    Posts
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    Thank you for the tips. I will try. I have a 8 subjest assicnments with a total of 8*6 questions. I have to submit it on monday. They give 2 days to complete these.
    The big problem i face is lack of time. Thank you
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