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Math Help - Help w/ General Solution

  1. #1
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    Help w/ General Solution

    Need assistance arriving at this general solution for a particular ODE:

    e^{y^{3}}=csc(x)y^{2}y'
    => y' = \frac{e^{y^{3}}}{csc(x)y^{2}}
    \frac{dy}{dx}= \frac{e^{y^{3}}}{csc(x)y^{2}}
    ...??
    =>3cos(x)+C = e^{-y^{3}}

    Ty
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  2. #2
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    Quote Originally Posted by mmattson07 View Post
    Need assistance arriving at this general solution for a particular ODE:

    e^{y^{3}}=csc(x)y^{2}y'
    => y' = \frac{e^{y^{3}}}{csc(x)y^{2}}
    \frac{dy}{dx}= \frac{e^{y^{3}}}{csc(x)y^{2}}
    ...??
    =>3cos(x)+C = e^{-y^{3}}

    Ty
    That solution looks fine. But if you want to make y the subject, start by taking the log of both sides.
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  3. #3
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    Could you maybe show a few steps as to hint how to arrive at that solution?

    Thanks.
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  4. #4
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    Quote Originally Posted by mmattson07 View Post
    Could you maybe show a few steps as to hint how to arrive at that solution?

    Thanks.
    Did you try the first step I suggested? Please show what you've tried.
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  5. #5
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    Oh I thought you meant take the log of both sides if i wanted the soltuon in the form y=
    So take the log of both sides of the original DE? Wouldn't that just make things uglier? I tried solving using Separation of Variables but I got stuck where indicated...
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  6. #6
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    Quote Originally Posted by mmattson07 View Post
    Oh I thought you meant take the log of both sides if i wanted the soltuon in the form y=
    So take the log of both sides of the original DE? Wouldn't that just make things uglier? I tried solving using Separation of Variables but I got stuck where indicated...
    NO!
    Quote Originally Posted by mmattson07 View Post
    Need assistance arriving at this general solution for a particular ODE:

    e^{y^{3}}=csc(x)y^{2}y'
    => y' = \frac{e^{y^{3}}}{csc(x)y^{2}}
    \frac{dy}{dx}= \frac{e^{y^{3}}}{csc(x)y^{2}}
    ...??
    =>3cos(x)+C = e^{-y^{3}} Mr F says: Take log to the base e of both sides of this line!

    Ty
    Look, if you're studying DE's this should not be a difficult thing to do. Do what I've said to do, post what you do, say where you're stuck.
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