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Homework Help: Science & engineering math: system of differential equations

  1. Mar 18, 2012 #1
    1. The problem statement, all variables and given/known data

    Solve the system of differential equations:
    y'(t) + z(t) = t
    y"(t) - z(t) = e-t
    Subject to y(0) = 3, y'(0) = -2, and z(0) = 0

    2. Relevant equations

    My professor did an example in class that was much simpler and solved it using Kramer's rule.

    3. The attempt at a solution
    I don't know how to start it. I thought about rearranging the equations so that one was equal to y'(t) and the other was equal to z(t), but I'm not sure that would work...
  2. jcsd
  3. Mar 18, 2012 #2


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    Homework Helper

    What about adding the equations so as z(t) cancels?

  4. Mar 18, 2012 #3


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    Gold Member

    I would definitely start off as ehild has suggested.
  5. Mar 18, 2012 #4


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    Science Advisor

    There is, however, a problem with the entire exercise. Doing as ehild suggests gives you a second order differential equation in y only which you can solve and then use the initial conditions to give a specific solution for y. But there is no derivative of z in these equations- once you know y, z is fixed and you have no constant to choose to make z(0)= 0. Was one or both of those "z"s supposed to be z'? If not then any one of the three conditions, y(0)= 3, y'(0)= -2, z(0)=n 0, can be dropped to give a solution but there is not y, z, satisfying the equations and all three of the conditions.
  6. Mar 18, 2012 #5
    Oh my gosh yes there was supposed to be a z' in the first equation
    So it is: y'(t) + z'(t) = t
    The second equation is correct though, so sorry for any confusion!!
  7. Mar 18, 2012 #6


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    Homework Helper

    Then you can integrate the first equation and add to the second.

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