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Math Help - differential equations problem

  1. #1
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    differential equations problem

    I haven't dealt with differential equations in a while so I completely forget how to do this problem.

    Given dx/dt=y and dy/dt=x

    Verify that f(t)=Ce^t+De^-t and g(t)=Ce^t - De^-t give a solution to the system of differential equations, where C and D are arbitrary constants.

    Thanks!
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  2. #2
    Senior Member DeMath's Avatar
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    Quote Originally Posted by morganfor View Post
    I haven't dealt with differential equations in a while so I completely forget how to do this problem.

    Given dx/dt=y and dy/dt=x

    Verify that f(t)=Ce^t+De^-t and g(t)=Ce^t - De^-t give a solution to the system of differential equations, where C and D are arbitrary constants.

    Thanks!
    Have уou to solve a system of diff. equations  \left\{ \begin{gathered}\frac{{dx}}{{dt}} = y, \hfill \\\frac{{dy}}{{dt}} = x. \hfill \\ \end{gathered}  \right. ?

    Differentiate, for example, the first equation \frac{{{d^2}x}}<br />
{{d{t^2}}} - \frac{{dy}}{{dt}} = 0 and because \frac{dy}{dt} = x
    you get a simple diff. equation x''\left( t \right) - x\left( t \right) = 0

    I think you know what you need to do next.
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  3. #3
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    Actually, I'm having some trouble differentiating x''-x=0. I can't quite seem to get the e's in my equation.
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  4. #4
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    Quote Originally Posted by morganfor View Post
    Actually, I'm having some trouble differentiating x''-x=0. I can't quite seem to get the e's in my equation.
    \frac{d^2 x}{dt^2} - x = 0 is a linear second order differential equation with constant coefficients. Have you studied that type of DE before?
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  5. #5
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    I'm sure I have but it's been atleast 3 years I just need a little refresher
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  6. #6
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    Quote Originally Posted by morganfor View Post
    I'm sure I have but it's been atleast 3 years I just need a little refresher
    Have you tried using Google to get that refresher? Keywords:

    linear second order differential equation constant coefficients
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  7. #7
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    yes i did actually - i forgot to add that to the thread earlier.

    thanks everyone!
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  8. #8
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    Quote Originally Posted by morganfor View Post
    yes i did actually - i forgot to add that to the thread earlier.

    thanks everyone!
    Morganfor, the differential equations videos at Khan Academy are excellent if you're looking for a refresher. Good luck
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  9. #9
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    This problem does not ask you to solve the equations, just show that the given functions satisfy the equations. That's much simpler.
    If x(t)=Ce^t+De^{-t} and y(t)=Ce^t - De^{-t}, what are dx/dt and dy/dt?
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  10. #10
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    i apologize that i'm still stuck on this problem!

    as far as verifying that the given solutions are correct - I'm sure I'm missing a simple step but I can't seem to differentiate f(t)=Ce^t+De^-t and g(t)=Ce^t-De^t to give me y and x. I'm confused as to which substitutions I need to make...
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