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Math Help - u and v are solutions

  1. #1
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    u and v are solutions

    Clearly u = cos x and v = sin x are solutions of y'' + y = 0. Show that  z = u^2 and z = uv are solutions of z''' + 4z' = 0


    I dont understand how to start this off. Im not asking for the answer just trying to understand what is going on or what to do.
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  2. #2
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    Is what's meant to be clear, clear? Just in case a picture helps...



    ... differentiating downwards.

    Spoiler:

    _________________________________________
    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
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  3. #3
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    Quote Originally Posted by onemore View Post
    Clearly u = cos x and v = sin x are solutions of y'' + y = 0. Show that  z = u^2 and z = uv are solutions of z''' + 4z' = 0


    I dont understand how to start this off. Im not asking for the answer just trying to understand what is going on or what to do.
    z= u^2= cos^2(x). What is (cos^2(x))'''+ 4(cos^2(x))'?

    z= uv= cos(x)sin(x). What is (cos(x)sin(x))'''+ 4(cos(x)sin(x))'?
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