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Homework Help: Not sure what to do with this DE problem

  1. Sep 8, 2013 #1
    1. The problem statement, all variables and given/known data
    Verify by substitution that each given function is a solution of the given differential equation. Throughout these problems, primes denote derivatives with respect to x.
    y'=3x2; y=x3+7

    2. Relevant equations

    3. The attempt at a solution
    Well obviously I see that the derivative of y=x3+7 is just 3x2, but what does it mean by verifying by substitution? :confused:
  2. jcsd
  3. Sep 8, 2013 #2


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    Homework Helper

    It means substitute [itex]y = x^3 + 7[/itex] into [itex]y' = 3x^2[/itex] to get [itex](x^3 + 7)' = 3x^2[/itex] and then confirm that the left hand side does in fact equal the right hand side. In this case it obviously does, so there's nothing more to do. Although I suppose you could expressly state that [itex](x^3 + 7)' = (x^3)' + (7)' = 3x^2 + 0 = 3x^2[/itex].
  4. Sep 8, 2013 #3
    Why do they make me even do this...?
  5. Sep 8, 2013 #4


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    Staff Emeritus
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    Homework Helper

    Usually, they don't anticipate the student having any problem verifying an equation given its solution.
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