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Math Help - Diferential equations

  1. #1
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    Diferential equations

    Find the general solution of the second-order inhomogeneous differential equation

    y''+3y'+2y=

    I have got lamda equals to -2 and -1 and then i got


    y(x)=Ae^(-2x)+Be^(-2x)

    I am not too sure what to do after this.. help would be appreciated thx
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  2. #2
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    Hello, rajr!

    Find the general solution of the second-order inhomogeneous differential equation:

    . . . y''+3y'+2y\:=\:e^{2x}\cos x


    I have got: . \lambda \:=\:\text{-}1,\:\text{-}2

    then i got: . y(x)\:=\:C_1e^{-x}+C_2e^{-2x}

    I am not too sure what to do after this.
    What methods do you know? . . . . \begin{array}{c}\text{Undetermined Coefficients?} \\ \text{Variation of Parameters?} \\ \text{Method of Operators?} \end{array}

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  3. #3
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    undetermined coefficients
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  4. #4
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    Quote Originally Posted by rajr View Post
    Find the general solution of the second-order inhomogeneous differential equation

    y''+3y'+2y=

    I have got lamda equals to -2 and -1 and then i got


    y(x)=Ae^(-2x)+Be^(-2x)

    I am not too sure what to do after this.. help would be appreciated thx
    Try y(x)= e^{2x}(C cos(x)+ D sin(x))
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  5. #5
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    i have to find y' and y'' for this right!
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  6. #6
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    i got y' to be A (2e^(2x)sin(x))+a (e^(2x)cox(x))+B(2e^(2x)cosx)-B(sinxe^(2x))
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  7. #7
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    Quote Originally Posted by rajr View Post
    i got y' to be A (2e^(2x)sin(x))+a (e^(2x)cox(x))+B(2e^(2x)cosx)-B(sinxe^(2x))
    I think it is simpler not to multiply it out. If y= e^{2x}(A cos(x)+ B sin(x)) then y'= 2e^{2x}(A cos(x)+ B sin(x))+ e^{2x}(-A sin(x)+ B cos(x))
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  8. #8
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    Can some one check my solution

    can any one check whether my answers are right:
    y'' = 2e^(2x)[(2A+B)COSX-(A+2B)SINX]-e^(2x)[(2A+B)SINX + (A+2B)COSX]

    AND THEN WHEN I SUBSTITUED THE Y,Y' AND Y'' AND I GOT EQUATIONS AND THEY ARE

    13A+7B = 1
    -7A-9B = 0

    AM I RIGHT..HELP WOULD BE APPRECIATED THANKS
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