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Math Help - Slope Field Help?

  1. #1
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    Exclamation Slope Field Help?

    Here's the problem:

    At any point of intersection of a solution curve of the d.e. y'=x+y and the line x+y=0, the function y at that point
    (a) is equal to 0
    (b) is a local maximum
    (c) has a local minimum
    (d) has a point of inflection
    (e) has a discontinuity

    First, what does "d.e." mean? Derivative?
    Second, I have no clue how to figure this out, so any help would be much appreciated!
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  2. #2
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    Quote Originally Posted by summermagic View Post
    Here's the problem:

    At any point of intersection of a solution curve of the d.e. y'=x+y and the line x+y=0, the function y at that point
    (a) is equal to 0
    (b) is a local maximum
    (c) has a local minimum
    (d) has a point of inflection
    (e) has a discontinuity

    First, what does "d.e." mean? Derivative?
    Second, I have no clue how to figure this out, so any help would be much appreciated!
    DE = Differential Equation.
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  3. #3
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    Quote Originally Posted by summermagic View Post
    Here's the problem:

    At any point of intersection of a solution curve of the d.e. y'=x+y and the line x+y=0, the function y at that point
    (a) is equal to 0
    (b) is a local maximum
    (c) has a local minimum
    (d) has a point of inflection
    (e) has a discontinuity

    First, what does "d.e." mean? Derivative?
    Second, I have no clue how to figure this out, so any help would be much appreciated!

    The d.e. y'=x+y can be solved using the intergrating factor method.

    Integrating factor - Wikipedia, the free encyclopedia

    I tried this and got an integrating factor of exp(-x)

    You can also maybe use the fact that y'=x+y and x+y=0

    implies y' = 0
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