Non-linear differential equation example

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I'm dealing with the following differential equation



$fracdydx = frac(y-x)(a-by)(1-fracbax)(a-2by+bx)$ with $x,y in [0, fracab]$



Can anyone help me with the non trivial solution?



Thanks.




differential-equations




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  • 1




    How can we show you your mistake if you don't show us your working?
    – Mattos
    Aug 6 at 3:54










  • I didn't mean to check my working, I was wondering whether the solution is correct or not.
    – PK K
    Aug 6 at 4:18






  • 1




    @PK.K : See my answer. For information : A solution, but not all solutions, is $$y=frac(a+b)x+aa+2b$$
    – JJacquelin
    Aug 6 at 6:39











  • @PK.K . HINT : another much simpler solution is obvious. Don't you see it ?
    – JJacquelin
    Aug 6 at 7:19










  • Yes the (1,0) solution is obvious but it is a corner solution and not desirable for the application I'm looking for.
    – PK K
    Aug 7 at 23:40















up vote
0
down vote

favorite
3












I'm dealing with the following differential equation



$fracdydx = frac(y-x)(a-by)(1-fracbax)(a-2by+bx)$ with $x,y in [0, fracab]$



Can anyone help me with the non trivial solution?



Thanks.




differential-equations




share|cite|improve this question

















  • 1




    How can we show you your mistake if you don't show us your working?
    – Mattos
    Aug 6 at 3:54










  • I didn't mean to check my working, I was wondering whether the solution is correct or not.
    – PK K
    Aug 6 at 4:18






  • 1




    @PK.K : See my answer. For information : A solution, but not all solutions, is $$y=frac(a+b)x+aa+2b$$
    – JJacquelin
    Aug 6 at 6:39











  • @PK.K . HINT : another much simpler solution is obvious. Don't you see it ?
    – JJacquelin
    Aug 6 at 7:19










  • Yes the (1,0) solution is obvious but it is a corner solution and not desirable for the application I'm looking for.
    – PK K
    Aug 7 at 23:40













up vote
0
down vote

favorite
3









up vote
0
down vote

favorite
3






3





I'm dealing with the following differential equation



$fracdydx = frac(y-x)(a-by)(1-fracbax)(a-2by+bx)$ with $x,y in [0, fracab]$



Can anyone help me with the non trivial solution?



Thanks.




differential-equations




share|cite|improve this question













I'm dealing with the following differential equation



$fracdydx = frac(y-x)(a-by)(1-fracbax)(a-2by+bx)$ with $x,y in [0, fracab]$



Can anyone help me with the non trivial solution?



Thanks.





differential-equations





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 8 at 5:33
























asked Aug 6 at 3:36









PK K

193




193







  • 1




    How can we show you your mistake if you don't show us your working?
    – Mattos
    Aug 6 at 3:54










  • I didn't mean to check my working, I was wondering whether the solution is correct or not.
    – PK K
    Aug 6 at 4:18






  • 1




    @PK.K : See my answer. For information : A solution, but not all solutions, is $$y=frac(a+b)x+aa+2b$$
    – JJacquelin
    Aug 6 at 6:39











  • @PK.K . HINT : another much simpler solution is obvious. Don't you see it ?
    – JJacquelin
    Aug 6 at 7:19










  • Yes the (1,0) solution is obvious but it is a corner solution and not desirable for the application I'm looking for.
    – PK K
    Aug 7 at 23:40













  • 1




    How can we show you your mistake if you don't show us your working?
    – Mattos
    Aug 6 at 3:54










  • I didn't mean to check my working, I was wondering whether the solution is correct or not.
    – PK K
    Aug 6 at 4:18






  • 1




    @PK.K : See my answer. For information : A solution, but not all solutions, is $$y=frac(a+b)x+aa+2b$$
    – JJacquelin
    Aug 6 at 6:39











  • @PK.K . HINT : another much simpler solution is obvious. Don't you see it ?
    – JJacquelin
    Aug 6 at 7:19










  • Yes the (1,0) solution is obvious but it is a corner solution and not desirable for the application I'm looking for.
    – PK K
    Aug 7 at 23:40








1




1




How can we show you your mistake if you don't show us your working?
– Mattos
Aug 6 at 3:54




How can we show you your mistake if you don't show us your working?
– Mattos
Aug 6 at 3:54












I didn't mean to check my working, I was wondering whether the solution is correct or not.
– PK K
Aug 6 at 4:18




I didn't mean to check my working, I was wondering whether the solution is correct or not.
– PK K
Aug 6 at 4:18




1




1




@PK.K : See my answer. For information : A solution, but not all solutions, is $$y=frac(a+b)x+aa+2b$$
– JJacquelin
Aug 6 at 6:39





@PK.K : See my answer. For information : A solution, but not all solutions, is $$y=frac(a+b)x+aa+2b$$
– JJacquelin
Aug 6 at 6:39













@PK.K . HINT : another much simpler solution is obvious. Don't you see it ?
– JJacquelin
Aug 6 at 7:19




@PK.K . HINT : another much simpler solution is obvious. Don't you see it ?
– JJacquelin
Aug 6 at 7:19












Yes the (1,0) solution is obvious but it is a corner solution and not desirable for the application I'm looking for.
– PK K
Aug 7 at 23:40





Yes the (1,0) solution is obvious but it is a corner solution and not desirable for the application I'm looking for.
– PK K
Aug 7 at 23:40











1 Answer
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To your question : "whether my solution is correct or not ?" the answer is obviously NO.



Putting your solution $$y(x)= fraca2b +fracx2$$
into
$$fracdydx = frac(y-x)(a-by)(1-fracbax)(a-2by+bx)$$
shows
$$(a-2by+bx)=0$$
at denominator.






share|cite|improve this answer





















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    up vote
    0
    down vote













    To your question : "whether my solution is correct or not ?" the answer is obviously NO.



    Putting your solution $$y(x)= fraca2b +fracx2$$
    into
    $$fracdydx = frac(y-x)(a-by)(1-fracbax)(a-2by+bx)$$
    shows
    $$(a-2by+bx)=0$$
    at denominator.






    share|cite|improve this answer

























      up vote
      0
      down vote













      To your question : "whether my solution is correct or not ?" the answer is obviously NO.



      Putting your solution $$y(x)= fraca2b +fracx2$$
      into
      $$fracdydx = frac(y-x)(a-by)(1-fracbax)(a-2by+bx)$$
      shows
      $$(a-2by+bx)=0$$
      at denominator.






      share|cite|improve this answer























        up vote
        0
        down vote










        up vote
        0
        down vote









        To your question : "whether my solution is correct or not ?" the answer is obviously NO.



        Putting your solution $$y(x)= fraca2b +fracx2$$
        into
        $$fracdydx = frac(y-x)(a-by)(1-fracbax)(a-2by+bx)$$
        shows
        $$(a-2by+bx)=0$$
        at denominator.






        share|cite|improve this answer













        To your question : "whether my solution is correct or not ?" the answer is obviously NO.



        Putting your solution $$y(x)= fraca2b +fracx2$$
        into
        $$fracdydx = frac(y-x)(a-by)(1-fracbax)(a-2by+bx)$$
        shows
        $$(a-2by+bx)=0$$
        at denominator.







        share|cite|improve this answer













        share|cite|improve this answer



        share|cite|improve this answer











        answered Aug 6 at 6:13









        JJacquelin

        40.2k21649




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