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Math Help - Linear Algebra equation: please help!

  1. #1
    t16
    Guest

    Linear Algebra equation: please help!

    Matrix A:
    1 1
    4 1

    x' = Ax

    ( x' = Derivative of x )

    Solve for the general solution to the system.


    Above is the equation. I'm 90% sure it's linear algebra and supposedly a rather simple equation, however I've no idea how to do it as I've not taken linear algebra yet. Bit desperate for an answer to it, any help would be greatly appreciated!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by t16 View Post
    Matrix A:
    1 1
    4 1

    x' = Ax

    ( x' = Derivative of x )

    Solve for the general solution to the system.


    Above is the equation. I'm 90% sure it's linear algebra and supposedly a rather simple equation, however I've no idea how to do it as I've not taken linear algebra yet. Bit desperate for an answer to it, any help would be greatly appreciated!
    Let:

    x={x_1 \brack n_2} ,

    then we have a pair of coupled ODEs:

    x_1'=x_1+x_2

    x_2'=4x_1+x_2

    Differentiate the first equation again to get:

    x_1''=x_1'+x_2'=x_1'+4x_1+x_2=2x_1'+3x_1

    which is a homogeneous linear 2nd order ODE which you should be able to solve for x_1.

    Now do the same to get the 2nd order ODE for x_2.

    RonL
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