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First and Second Order Differential Equation

  1. Apr 15, 2008 #1
    1. The problem statement, all variables and given/known data

    a) Show that phi(t) = e^2t is a solution of y' - 2y = 0 and that C*phi(t) is also a solution for any constant C

    b) Show that phi(t) = 1/t is a solution of y' + y^2 = 0 for t>0 but that y = c*phi(t) is not a solution unless c = 0 or c = 1

    2. Relevant equations

    What do they mean by "show'?

    3. The attempt at a solution

    a) dy/2y = dt

    (1/2)ln(y) = t + C

    y = e^(2t + c) = Ce^2t, where c is any constant

    Now what?

    b) -dy/y^2 = dt

    1/y = t + C

    y = 1/(t + C)

    Again, how do i show?
  2. jcsd
  3. Apr 15, 2008 #2


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    Hi aznkid310! :smile:
    That's it! You've done it! :smile:

    Again, that's it … except of course you still have to make the obvious remark that C/t is not a solution! :smile:
    I think they just mean "prove". :smile:

    Alternatively, they may mean "no need to pretend you don't know the answer … just plug the answer straight in to the original equation and confirm that it works" :rolleyes:

    Better ask your teacher/tutor/professor which one it is! :smile:
  4. Apr 15, 2008 #3


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    'Show' just means substitute the given solutions into the differential equations and verify that they work or not. You don't have to solve the differential equation.
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