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Decouple the following equations?

Posted 2 months ago
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I have two couple equations and I want to decouple it. How can I do it? any help will be appreciated.

eq1 = k*X''[Y] + Bi*(Z[Y] - X[Y]) == Subscript[U, p]/Subscript[U, m];
eq2 = Z''[Y] - Bi*(Z[Y] - X[Y]) == 0;
Posted 2 months ago

Once again with proper formatting and some tiny comments:

eq1 = k*X''[Y] + Bi*(Z[Y] - X[Y]) == Subscript[U, p]/Subscript[U, m];
eq2 = Z''[Y] - Bi*(Z[Y] - X[Y]) == 0;

Solve eq2 first:

sol2 = Solve[eq2, Z[Y]]

Insert solution of eq2 into eq1:

eq3 = Simplify[eq1 /. Flatten[sol2]]

Flatten is used to remove the extra {}. Final results is:

(* k (X^\[Prime]\[Prime])[Y] + (Z^\[Prime]\[Prime])[
   Y] == Subscript[U, p]/Subscript[U, m] *)
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