Laplace Transformation of $y''+5y'+6y=2e^{-t}, y(0)=1, y'(0)=3$












-2












$begingroup$


Laplace Transformation of



$$y''+5y'+6y=2e^{-t}, quad y(0)=1, y'(0)=3 $$



$$s^2Y(s)-s+5Y(s)=frac{2}{s+1}+s+8 $$



$$frac{A}{s+1}+frac{B}{s+3}+frac{C}{s+2}=s^2+9s+10 $$



$A=1, B=-4, C=4 $



$$y(t) = e^{-t}-4e^{-3t}+4e^{-2t} $$



Am I right?






ordinary-differential-equations







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  • $begingroup$
    It's really difficult to tell without you formatting your text properly... I'd edit it but I can't make heads or tails of some portions. Please read math.meta.stackexchange.com/questions/5020/…
    $endgroup$
    – Eevee Trainer
    Dec 7 '18 at 6:31










  • $begingroup$
    If you're going to post multiple questions, at least try to learn a little bit of formatting
    $endgroup$
    – Dylan
    Dec 7 '18 at 6:43
















-2












$begingroup$


Laplace Transformation of



$$y''+5y'+6y=2e^{-t}, quad y(0)=1, y'(0)=3 $$



$$s^2Y(s)-s+5Y(s)=frac{2}{s+1}+s+8 $$



$$frac{A}{s+1}+frac{B}{s+3}+frac{C}{s+2}=s^2+9s+10 $$



$A=1, B=-4, C=4 $



$$y(t) = e^{-t}-4e^{-3t}+4e^{-2t} $$



Am I right?






ordinary-differential-equations







share|cite|improve this question











$endgroup$












  • $begingroup$
    It's really difficult to tell without you formatting your text properly... I'd edit it but I can't make heads or tails of some portions. Please read math.meta.stackexchange.com/questions/5020/…
    $endgroup$
    – Eevee Trainer
    Dec 7 '18 at 6:31










  • $begingroup$
    If you're going to post multiple questions, at least try to learn a little bit of formatting
    $endgroup$
    – Dylan
    Dec 7 '18 at 6:43














-2












-2








-2





$begingroup$


Laplace Transformation of



$$y''+5y'+6y=2e^{-t}, quad y(0)=1, y'(0)=3 $$



$$s^2Y(s)-s+5Y(s)=frac{2}{s+1}+s+8 $$



$$frac{A}{s+1}+frac{B}{s+3}+frac{C}{s+2}=s^2+9s+10 $$



$A=1, B=-4, C=4 $



$$y(t) = e^{-t}-4e^{-3t}+4e^{-2t} $$



Am I right?






ordinary-differential-equations







share|cite|improve this question











$endgroup$




Laplace Transformation of



$$y''+5y'+6y=2e^{-t}, quad y(0)=1, y'(0)=3 $$



$$s^2Y(s)-s+5Y(s)=frac{2}{s+1}+s+8 $$



$$frac{A}{s+1}+frac{B}{s+3}+frac{C}{s+2}=s^2+9s+10 $$



$A=1, B=-4, C=4 $



$$y(t) = e^{-t}-4e^{-3t}+4e^{-2t} $$



Am I right?






ordinary-differential-equations




ordinary-differential-equations






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 7 '18 at 6:44









Dylan

12.6k31026




12.6k31026










asked Dec 7 '18 at 6:29









sumthatup11sumthatup11

11




11












  • $begingroup$
    It's really difficult to tell without you formatting your text properly... I'd edit it but I can't make heads or tails of some portions. Please read math.meta.stackexchange.com/questions/5020/…
    $endgroup$
    – Eevee Trainer
    Dec 7 '18 at 6:31










  • $begingroup$
    If you're going to post multiple questions, at least try to learn a little bit of formatting
    $endgroup$
    – Dylan
    Dec 7 '18 at 6:43


















  • $begingroup$
    It's really difficult to tell without you formatting your text properly... I'd edit it but I can't make heads or tails of some portions. Please read math.meta.stackexchange.com/questions/5020/…
    $endgroup$
    – Eevee Trainer
    Dec 7 '18 at 6:31










  • $begingroup$
    If you're going to post multiple questions, at least try to learn a little bit of formatting
    $endgroup$
    – Dylan
    Dec 7 '18 at 6:43
















$begingroup$
It's really difficult to tell without you formatting your text properly... I'd edit it but I can't make heads or tails of some portions. Please read math.meta.stackexchange.com/questions/5020/…
$endgroup$
– Eevee Trainer
Dec 7 '18 at 6:31




$begingroup$
It's really difficult to tell without you formatting your text properly... I'd edit it but I can't make heads or tails of some portions. Please read math.meta.stackexchange.com/questions/5020/…
$endgroup$
– Eevee Trainer
Dec 7 '18 at 6:31












$begingroup$
If you're going to post multiple questions, at least try to learn a little bit of formatting
$endgroup$
– Dylan
Dec 7 '18 at 6:43




$begingroup$
If you're going to post multiple questions, at least try to learn a little bit of formatting
$endgroup$
– Dylan
Dec 7 '18 at 6:43










1 Answer
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$begingroup$

I'm not sure if there's a typo in the first line or not - your question is very poorly formatted and you skipped a couple steps, but it should be



$$ (s^2 Y - s - 3) + 5(sY - 1) + 6Y = frac{2}{s+1} $$



$$ implies (s^2 + 5s+6)Y = frac{2}{s+1} + s + 8 = frac{s^2+9s+10}{s+1} $$



Then



$$ Y(s) = frac{s^2+9s+10}{(s+1)(s+2)(s+3)} = frac{A}{s+1} + frac{B}{s+2} + frac{C}{s+3} $$



I believe the answer is correct.






share|cite|improve this answer









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    $begingroup$

    I'm not sure if there's a typo in the first line or not - your question is very poorly formatted and you skipped a couple steps, but it should be



    $$ (s^2 Y - s - 3) + 5(sY - 1) + 6Y = frac{2}{s+1} $$



    $$ implies (s^2 + 5s+6)Y = frac{2}{s+1} + s + 8 = frac{s^2+9s+10}{s+1} $$



    Then



    $$ Y(s) = frac{s^2+9s+10}{(s+1)(s+2)(s+3)} = frac{A}{s+1} + frac{B}{s+2} + frac{C}{s+3} $$



    I believe the answer is correct.






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      I'm not sure if there's a typo in the first line or not - your question is very poorly formatted and you skipped a couple steps, but it should be



      $$ (s^2 Y - s - 3) + 5(sY - 1) + 6Y = frac{2}{s+1} $$



      $$ implies (s^2 + 5s+6)Y = frac{2}{s+1} + s + 8 = frac{s^2+9s+10}{s+1} $$



      Then



      $$ Y(s) = frac{s^2+9s+10}{(s+1)(s+2)(s+3)} = frac{A}{s+1} + frac{B}{s+2} + frac{C}{s+3} $$



      I believe the answer is correct.






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        I'm not sure if there's a typo in the first line or not - your question is very poorly formatted and you skipped a couple steps, but it should be



        $$ (s^2 Y - s - 3) + 5(sY - 1) + 6Y = frac{2}{s+1} $$



        $$ implies (s^2 + 5s+6)Y = frac{2}{s+1} + s + 8 = frac{s^2+9s+10}{s+1} $$



        Then



        $$ Y(s) = frac{s^2+9s+10}{(s+1)(s+2)(s+3)} = frac{A}{s+1} + frac{B}{s+2} + frac{C}{s+3} $$



        I believe the answer is correct.






        share|cite|improve this answer









        $endgroup$



        I'm not sure if there's a typo in the first line or not - your question is very poorly formatted and you skipped a couple steps, but it should be



        $$ (s^2 Y - s - 3) + 5(sY - 1) + 6Y = frac{2}{s+1} $$



        $$ implies (s^2 + 5s+6)Y = frac{2}{s+1} + s + 8 = frac{s^2+9s+10}{s+1} $$



        Then



        $$ Y(s) = frac{s^2+9s+10}{(s+1)(s+2)(s+3)} = frac{A}{s+1} + frac{B}{s+2} + frac{C}{s+3} $$



        I believe the answer is correct.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 7 '18 at 6:51









        DylanDylan

        12.6k31026




        12.6k31026






























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