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Math Help - Separable equations (variables)

  1. #1
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    Separable equations (variables)

    Out of these equations: Separable equations (variables)-capture3.jpgwhich one(s) are the variables not separable? Now I think II and III can be separated but I can not. Is this right? The way I came to this conclusion is by simply testing each one. I could not figure out a way to separate the variables for I. but for II and III I could. I might just be completely missing something for I and maybe it can be separate, maybe the other two can't and I just did them wrong! I'm not sure. As I said I couldn't figure out a way to separate I, but for II I had: d^2y/y*dy= 3x+dx after separating the variables and for III I had: dx/x=y^2/y-dy I'm not confident at all about how I separated them, it just doesn't seem right.
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  2. #2
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    Re: Separable equations (variables)

    You are incorrect in your reasoning above. That's all I'm telling you.
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  3. #3
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    Re: Separable equations (variables)

    Differential equations have to be first-order to be separable, don't they?

    - Hollywood
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    Re: Separable equations (variables)

    Quote Originally Posted by hollywood View Post
    Differential equations have to be first-order to be separable, don't they?

    - Hollywood
    So then I and III are separable?
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    Re: Separable equations (variables)

    Quote Originally Posted by canyouhelp View Post
    So then I and III are separable?
    Stop Guessing!!

    I is trivially separable.

    since you believe it is separable please write III in separated form for us.
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    Re: Separable equations (variables)

    Quote Originally Posted by romsek View Post
    Stop Guessing!!

    I is trivially separable.

    since you believe it is separable please write III in separated form for us.
    For III I had: dx/x=y^2/y-dy ..but I think I separated it wrong :/
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    Re: Separable equations (variables)

    Quote Originally Posted by canyouhelp View Post
    For III I had: dx/x=y^2/y-dy ..but I think I separated it wrong :/
    $\dfrac{dy}{dx}=y^2+yx = y(y+x)$

    $\dfrac{dy}{y}=(y+x)~dx$

    how are you going to separate that?

    You're not.
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    Re: Separable equations (variables)

    Quote Originally Posted by romsek View Post
    $\dfrac{dy}{dx}=y^2+yx = y(y+x)$

    $\dfrac{dy}{y}=(y+x)~dx$

    how are you going to separate that?

    You're not.
    Oh, okay. Thanks!
    So is it impossible to separate #2 because it's not first-order?
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    Re: Separable equations (variables)

    Quote Originally Posted by romsek View Post
    $\dfrac{dy}{dx}=y^2+yx = y(y+x)$

    $\dfrac{dy}{y}=(y+x)~dx$

    how are you going to separate that?

    You're not.
    So my answer should be II and III? because they both cannot be separated. Or can II be separated? I tried to above, but that was probably just really wrong.
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  10. #10
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    Re: Separable equations (variables)

    I think we've decided that II is second-order, so can not be separated. And III is first-order, so the question at least makes sense, but it can't be separated. So only I can be separated.

    In your original post, you marked I only, but your argument was for II and III, the exact opposite.

    - Hollywood
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    Re: Separable equations (variables)

    Quote Originally Posted by hollywood View Post
    I think we've decided that II is second-order, so can not be separated. And III is first-order, so the question at least makes sense, but it can't be separated. So only I can be separated.

    In your original post, you marked I only, but your argument was for II and III, the exact opposite.

    - Hollywood
    Yea, sorry. I miss-read the question thinking it was asking which ones were separable. But thank you!
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