Message Boards Message Boards

Help solving two equations analytically?

H Li
Posted 2 years ago

I can solve this for X and Y if I put in numeric values for a,b,c,d,e,f,r,s,z, but I would like to solve for X, Y analytically. Is it possible? The restrictions are: a,b,c,d,e,f,r,s,z,s,X,Y are all positive real numbers, and a>X>Y>b>0.

soln = Solve[{
   -(a - X)/c + (X - Y)/e + s^2*X*(X - Y)/(r + f) - 
     0.5*s^2*f*(X - Y)^2/(r + f)^2 == 
    0 , (Y - b)/d - (X - Y)/e - s^2*Y*(X - Y)/(r + f) - 
     0.5*s^2*f*(X - Y)^2/(r + f)^2 == 0
   }, {X, Y}]
POSTED BY: H Li
1 Reply
Sort By:

I seem to get an analytical solution after a change of variables:

newEqs = {-(a - X)/c + (X - Y)/e + s^2*X*(X - Y)/(r + f) - 
     1/2*s^2*f*(X - Y)^2/(r + f)^2 == 
    0, (Y - b)/d - (X - Y)/e - s^2*Y*(X - Y)/(r + f) - 
     1/2*s^2*f*(X - Y)^2/(r + f)^2 == 0} /. Y -> X - Z
sol0 = Solve[newEqs, {X, Z}]
sol0 /. Z -> X - Y
POSTED BY: Gianluca Gorni
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Tag limit exceeded
Note: Only the first five people you tag will receive an email notification; the other tagged names will appear as links to their profiles.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract