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Thread: Linear , homogenous, separation and change of variables

  1. #16
    Junior Member romeobernard's Avatar
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    Re: Linear , homogenous, separation and change of variables

    Wait I will figure out.

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  2. #17
    Junior Member romeobernard's Avatar
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    Re: Linear , homogenous, separation and change of variables

    Like this?

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  3. #18
    MHF Contributor MarkFL's Avatar
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    Re: Linear , homogenous, separation and change of variables

    That's not quite standard linear form...check my post.
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  4. #19
    Junior Member romeobernard's Avatar
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    Re: Linear , homogenous, separation and change of variables

    Like this??

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  5. #20
    MHF Contributor MarkFL's Avatar
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    Re: Linear , homogenous, separation and change of variables

    No, go back and look at my post...you will see I wrote the equation in standard linear form, and then I computed the integrating factor.
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  6. #21
    Junior Member romeobernard's Avatar
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    Re: Linear , homogenous, separation and change of variables

    Or this?

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  7. #22
    MHF Contributor MarkFL's Avatar
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    Re: Linear , homogenous, separation and change of variables

    Yes, isn't that what I wrote?
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  8. #23
    Junior Member romeobernard's Avatar
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    Re: Linear , homogenous, separation and change of variables

    Hahaha yes i notice the r is transfer. Then after that? Integrating factor.?

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  9. #24
    MHF Contributor MarkFL's Avatar
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    Re: Linear , homogenous, separation and change of variables

    Yes, once you have the equation in standard linear form, you want to compute the integrating factor.
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  10. #25
    Junior Member romeobernard's Avatar
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    Re: Linear , homogenous, separation and change of variables

    This is what i get now.

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  11. #26
    MHF Contributor MarkFL's Avatar
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    Re: Linear , homogenous, separation and change of variables

    Okay, distribute the integrating factor on the left, and you will find the LHS can then be expressed as the derivative of the product of the integrating factor and the dependent variable r. This is the reason for computing the integrating factor in the first place.
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  12. #27
    Junior Member romeobernard's Avatar
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    Re: Linear , homogenous, separation and change of variables

    Okay now i get it.. heres my answer

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  13. #28
    Junior Member romeobernard's Avatar
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    Re: Linear , homogenous, separation and change of variables

    How about this one.? How to approach this question?

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  14. #29
    MHF Contributor MarkFL's Avatar
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    Re: Linear , homogenous, separation and change of variables

    You should really be starting new threads for new questions, and looking into using $\displaystyle \LaTeX$ to post your math instead of images (frequently sideways) of handwritten work.

    We are given:

    $\displaystyle (x+y)dx+(3x^2-y)dy=0$

    Is this ODE exact?
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  15. #30
    Junior Member romeobernard's Avatar
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    Re: Linear , homogenous, separation and change of variables

    I think its not exact.

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