analytical solution of coupled second order non linear ode

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I have two coupled non linear second order differential equation.



-y1"[x]=exp(k1(y1[x]-y2[x]))-exp(-k2(y1[x]-y2[x])),
-y2"[x]=-exp(k1(y1[x]-y2[x]))-exp(-k2(y1[x]-y2[x]))
I have been trying to solve it for past two weeks.Of course, I could get the numeric solution, but I am not able to get analytical solution . So, I was wondering if someone could help me how to solve this analytically so that i can get solution in terms of y1 and y2. Any solution to this problem would be of interest.










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    I have two coupled non linear second order differential equation.



    -y1"[x]=exp(k1(y1[x]-y2[x]))-exp(-k2(y1[x]-y2[x])),
    -y2"[x]=-exp(k1(y1[x]-y2[x]))-exp(-k2(y1[x]-y2[x]))
    I have been trying to solve it for past two weeks.Of course, I could get the numeric solution, but I am not able to get analytical solution . So, I was wondering if someone could help me how to solve this analytically so that i can get solution in terms of y1 and y2. Any solution to this problem would be of interest.










    share|cite|improve this question























      up vote
      -1
      down vote

      favorite









      up vote
      -1
      down vote

      favorite











      I have two coupled non linear second order differential equation.



      -y1"[x]=exp(k1(y1[x]-y2[x]))-exp(-k2(y1[x]-y2[x])),
      -y2"[x]=-exp(k1(y1[x]-y2[x]))-exp(-k2(y1[x]-y2[x]))
      I have been trying to solve it for past two weeks.Of course, I could get the numeric solution, but I am not able to get analytical solution . So, I was wondering if someone could help me how to solve this analytically so that i can get solution in terms of y1 and y2. Any solution to this problem would be of interest.










      share|cite|improve this question













      I have two coupled non linear second order differential equation.



      -y1"[x]=exp(k1(y1[x]-y2[x]))-exp(-k2(y1[x]-y2[x])),
      -y2"[x]=-exp(k1(y1[x]-y2[x]))-exp(-k2(y1[x]-y2[x]))
      I have been trying to solve it for past two weeks.Of course, I could get the numeric solution, but I am not able to get analytical solution . So, I was wondering if someone could help me how to solve this analytically so that i can get solution in terms of y1 and y2. Any solution to this problem would be of interest.







      differential-equations






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      asked Sep 6 at 6:28









      Akanksha

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