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Math Help - Differential equation question with limits

  1. #1
    Senior Member chella182's Avatar
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    Differential equation question with limits

    Sorry about the influx of my threads; panicking slightly about my distinct lack of ability when it comes to differential equations. I have the equation...

    y''+y'-2y=0 with y\rightarrow 0 as x\rightarrow +\infty and y(0)=2

    I got the auxilliary equation \lambda^2+\lambda -2=0 and factorised to get \lambda_1=-2 ; \lambda_2=1, so the general solution is...

    y=Ae^{-2x}+Be^{x}

    But I don't know how to find A and B with those conditions I get A+B=2 but that's about as far as I got. Any ideas?
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  2. #2
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    Quote Originally Posted by chella182 View Post
    Sorry about the influx of my threads; panicking slightly about my distinct lack of ability when it comes to differential equations. I have the equation...

    y''+y'-2y=0 with y\rightarrow 0 as x\rightarrow +\infty and y(0)=2

    I got the auxilliary equation \lambda^2+\lambda -2=0 and factorised to get \lambda_1=-2 ; \lambda_2=1, so the general solution is...

    y=Ae^{-2x}+Be^{x}

    But I don't know how to find A and B with those conditions I get A+B=2 but that's about as far as I got. Any ideas?
    check out what happens if B = 0
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  3. #3
    Senior Member chella182's Avatar
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    What happened to lengthy explanations on here? If B was zero then A would be 2...
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  4. #4
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    does y = 2e^{-2x} work ?

    did you even check it out?
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  5. #5
    Senior Member chella182's Avatar
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    No I didn't... I'm not getting why I would've though
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    y = Ae^{-2x} + Be^x

    \lim_{x \to \infty} Ae^{-2x} + Be^x = 0

    what is the only value of the constant B that will make the limit = 0 ?
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  7. #7
    Senior Member chella182's Avatar
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    0... but like... urgh. Forget it. I just wanted someone to walk me through the answer step by step.

    Unless you're telling me A=2 and B=0...
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