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Math Help - Differential

  1. #1
    Member ronaldo_07's Avatar
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    Differential


    Please help solve this question, Im having difficulty with it. Thanks.
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  2. #2
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    y_1'= 3y_1+ 4y_2
    y_2'= -2y_1- y_2

    Differentiate the first equation to get y_1"= 3y_1'+ 4y_2'. From the second equation, y_1"= 3y_1'+ 4(-2y_1- y_2)= 2y_1'- 8y_1- 4y_2.

    From the first equation again, 4y_2= y_1'- 3y_1 so y_1"= 3y_1'- 8y_1- (y_1'- 3y_1)= 2y_1'- 5y_1.

    That is, y_1"- 2y_1'+ 5y_1= 0. Can you solve that?

    That will have, of course, two constants in the general solution. To find y_2, use 4y_2= y_1'- 3y_1 so as not to introduce more constants.
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  3. #3
    Member ronaldo_07's Avatar
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    I got y=Ae^{(landa-2)x}+Be^{(landa+2)x} is this correct?
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