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Math Help - Third order DE-similiar to previous

  1. #1
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    Third order DE-similiar to previous

    y = c1 + c2cos x + c3sin x is the general solution of the differential equation y''' + y' = 0 on (-infinity, infinity). Find a member of the family that is a solution with initial conditions y(pi) = 0, y'(pi) = 2, and y''(pi) = -1.

    (1) What is the value of c1?
    (1) What is the value of c2?
    (1) What is the value of c3?


    I can't figure this one out for nothing!

    0=c1+c2cos(pi)+c3sin(pi)
    0=c1+c2(-1)+c3(0)
    0=c1-c2

    2=c1+c2(-sin(pi))+c3(cos(pi))
    2=c1+c2(0)-c3

    -1=c1+c2(cos(pi))+c3(-sin(pi))
    -1=c1-c2

    How would I solve the three equations to find each? I'm stuck here
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by latavee View Post
    y = c1 + c2cos x + c3sin x is the general solution of the differential equation y''' + y' = 0 on (-infinity, infinity). Find a member of the family that is a solution with initial conditions y(pi) = 0, y'(pi) = 2, and y''(pi) = -1.

    (1) What is the value of c1?
    (1) What is the value of c2?
    (1) What is the value of c3?


    I can't figure this one out for nothing!

    0=c1+c2cos(pi)+c3sin(pi)
    0=c1+c2(-1)+c3(0)
    0=c1-c2

    2=c1+c2(-sin(pi))+c3(cos(pi))
    2=c1+c2(0)-c3

    -1=c1+c2(cos(pi))+c3(-sin(pi))
    -1=c1-c2

    How would I solve the three equations to find each? I'm stuck here
    y(x)=c_1+c_2 \cos(x)+c_3\sin(x)

    y'(x)=-c_2\sin(x)+c_3\cos(x)

    y''(x)=-c_2\cos(x)-c_3\sin(x)

    CB
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