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Math Help - Determine whether the function is a solution of the DE?

  1. #1
    Junior Member xterminal01's Avatar
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    Determine whether the function is a solution of the DE?

    Determine whether the function is a solution of the differential equation
    y''' - 8y = 0

    (a) y = cos(2x)
    (b) y = e^(2x)

    What exactly is one suppose to do here? Is this suppose to be the third degree because we only covered first degree DE?
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  2. #2
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    Find y''' for each possibility and sub them back into the equation to check.

    Sound good?
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  3. #3
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    Well, you could differentiate the given functions and see if they satisfy the equation, i.e., you want to know if y''' = 8y.
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  4. #4
    Junior Member xterminal01's Avatar
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    cos(2x)-8y=0
    I end up with
    y = 1/8 cos(2 x) + C
    What should i do with this solution?


    Quote Originally Posted by pickslides View Post
    Find y''' for each possibility and sub them back into the equation to check.

    Sound good?
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  5. #5
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    Your derivative is not correct. y'= -2\cdot \sin(2x).
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  6. #6
    Junior Member xterminal01's Avatar
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    So i am suppose to replace a&b with Y''' or with 8(y)
    and what does the 3 ''' mean?

    Quote Originally Posted by lvleph View Post
    Your derivative is not correct. y'= -2\cdot \sin(2x).
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  7. #7
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    y''' means the third derivative. You are suppose to use the solutions in a) and b) and plug them in the original DEQ. If y from a) or b) satisfies y''' + 8y =0 then it is a solution to the DEQ.
    From a)
    y''' = 8\cos(2x)
    and so
    8\cos(2x) - 8cos(2x) = 0
    So, a) is a solution to the DEQ. Now, check if b) works.
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