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.
differential-equations
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up vote
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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.
differential-equations
add a comment |Â
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.
differential-equations
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
differential-equations
asked Sep 6 at 6:28
Akanksha
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12
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