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Basic Differential Equation (Should be Easy)

  1. Mar 16, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the general solution to the differential equation.

    dy/dx = 4 - y



    3. The attempt at a solution
    I only know how to solve them when one can multiply or divide by y. How does one take the integral of y with respect to x without the chain of y'? Thanks.
     
    Last edited: Mar 16, 2009
  2. jcsd
  3. Mar 16, 2009 #2

    lanedance

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    Hi EstimatedEyes

    what does y' mean? if = dy/dx, then you get 2 dy/dx = 4...?
     
  4. Mar 16, 2009 #3
    y' does mean dy/dx but I wrote the problem text down wrong. It should be:

    dy/dx = 4 - y
     
  5. Mar 16, 2009 #4

    lanedance

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    so any ideas? i think you can do this one by straight integration (with some substitution if needed...)

    you need to rearrange so all the y related terms are on one side & all the x on the other side then inetgrate both sides
     
  6. Mar 16, 2009 #5
    Yes, I know you have to isolate the variables but don't you need dy/dx multiplied to y in order to integrate?

    So you get integral(dy/dx + y) = 4x which would be easy if instead of y it was dy/dx*y but I do not know how to do it without the chain. It can't just be 1/2*y^2 can it?

    The answer the book has is y = 4 + Ce^-x. How does one arrive at this?
     
    Last edited: Mar 16, 2009
  7. Mar 16, 2009 #6
    Its a variable separable question.

    dy/(4 - y) = dx

    Integrate both sides. and solve for y
     
  8. Mar 16, 2009 #7
    Oh, now it's easy. Thank you Omerta6!
     
  9. Mar 16, 2009 #8
    Not a problem!
     
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