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Thread: Differential Equations

  1. #1 Differential Equations 
    Forum Bachelors Degree x(x-y)'s Avatar
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    I got a bit stuck on the second part of a question below, I'll show my first part working out as it's needed for the second part...

    Q: The variables x and y are related by the differential equation



    i) Use the substitution y=xz, where z is a function of x, to obtain the differential equation



    For this I got:







    So then part two says:

    ii) Find by integration the general solution of the differential equation A.

    I got this far on this question, and then got a bit stuck:



    I don't really know where to go from here... So any help would be appreciated! Thanks!


    "Nature doesn't care what we call it, she just does it anyway" - R. Feynman
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  3. #2  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    you have like 80% finished the whole thing,









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    "Mathematicians stand on each other's shoulders."- Carl Friedrich Gauss


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  4. #3  
    Forum Bachelors Degree x(x-y)'s Avatar
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    Hmmm... I did it and I got a solution slightly different to that: (following on from where I left off)







    Hmmm...
    "Nature doesn't care what we call it, she just does it anyway" - R. Feynman
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  5. #4  
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    it is really so difficult for me. but I indeed ger something from it
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  6. #5 Detail 
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    Quote Originally Posted by Heinsbergrelatz
    you have like 80% finished the whole thing,







    You have left out the constant of integration: whence:

    Quote Originally Posted by x(x-y)
    Hmmm... I did it and I got a solution slightly different to that: (following on from where I left off)







    Hmmm...
    You have simply got the solution in implicit form.

    Set for simplicity, solve with respect to , and you get the above explicit solution.

    The given equation, is of the general form: with being a Homogeneous Function of the th degree i.e. one satisfying: . In our case: , whence: , altogether a homogeneous function of the th degree.

    It could also assume the form: , i.e. we could consider as the unknown function and as the independent variable: . This could be solved by solving the above implicit solution wrt . Namely: . (A good exercise here would be to specify the domain of each of the four solutions given for by this formula!)
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  7. #6 differential equations 
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    Please solve the following differential equation step by step:

    (x^2 - 3y^2)xdx + (3x^2 - y^2)ydy = 0

    Thank you.....please help me !!!!!!!!!!!!!!!!!!!!!
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