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Differential Equations

  1. Nov 29, 2005 #1
    I am having trouble starting differential equations it says to find the general solution of such and i dont know where to get started on some of the.

    examples:

    dR
    --- = tan0 0=theta
    d0

    dy
    --- = 3x- 3y
    dx

    i dont want them answered as they are part of my assignment i just want help on how to go about starting to solve them.

    thank you

    Ryan
     
  2. jcsd
  3. Nov 29, 2005 #2
    A solution to a DE means that the value of 'x' or whatever the variable is, satisfies the equation. There can be infinitely many solutions to a DE!

    You should better consult your textbook. Or read Schaum's outline of DEs. I don't think anyone will solve these Qs here for you. We need to know that at least you tried.

    Hint: Separate Variables and Integrate!
     
  4. Nov 29, 2005 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    For the first one, rewrite it as
    [tex]dR= tan(\theta)d\theta[/tex]
    and integrate both sides.

    The second one is a "linear, first order" differential equation and I'll bet your textbook has some detailed information about those!
     
  5. Nov 29, 2005 #4
    ok thanks a lot that helps me out a lot.
     
  6. Nov 29, 2005 #5
    so for the dR = tan(0)d0

    would the answer be:

    y=-ln cos0+c
     
  7. Nov 29, 2005 #6
    and for:

    dy
    -- = 3x-3y
    dx

    would the answer be:

    y= ((3x^4)/4) - ((3y^4)/4)
     
  8. Nov 29, 2005 #7
    You can check your answer.

    for example)

    [tex] \frac{dy}{dx} = 3x-3y [/tex]
    This is saying that, a function exists [itex] y [/itex] that when you differentiate it with respect to [itex] x [/itex] then it is equal to [itex] 3x-3y [/itex]

    So how can you check your answer?

    Well your answer is saying that

    [tex] y= \frac{1}{4}3x^4 - \frac{1}{4}3y^4 [/tex]

    So if you differentiate your function.

    [tex] \frac{dy}{dx} = ? [/tex]

    Is that differentiated function equal to the right hand side (the [itex] 3x-3y[/itex])?

    Also what happened to the [itex] c [/itex] (don't forget the constant of integration) when you integrated? A general solution will have infinitely many solutions, so that [itex] c [/itex] is important. Otherwise it is not a general solution.
     
    Last edited: Nov 29, 2005
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