I have 3 equations Xi[1][x,t], Xi[2][t] , Phi[x, t], whose outputs are expressed in terms of variables {t, x, u}.
I want to generate X1 (an equation expressed in terms of variables {t,x,u} and constants C1, C2, ... , C6), similarly X2, X3, ... , X6. Please see an attachment on the attempts.
My goal is to write a syntax to select / pick the coefficient of the same constant from the 3 equations as shown below:
X1 = {{1/2 E^(-t \[Beta]) (1 + E^(2 t \[Beta])), 0, u (-((E^(-t \[Beta]) (-1 + E^(
t \[Beta])) (4 E^(t \[Beta]) \[Alpha] \[Beta] - \[Sigma]^2 - E^(t \[Beta]) \[Sigma]^2))/(2 \[Beta] \[Sigma]^2)) + 1/\[Sigma]^2 (2 x \[Beta] (1/ 2 E^(-t \[Beta]) (1 + E^(2 t \[Beta]))) +
2 x (E^(t \[Beta]) \[Beta] - 1/2 E^(-t \[Beta]) (1 + E^(2 t \[Beta])) \[Beta] )))},
X2 = {(E^(-t \[Beta]) (-1 + E^(2 t \[Beta])))/(2 \[Beta]), 0,
u (-((E^(-t \[Beta]) (-1 + E^(
t \[Beta])) (4 E^(
t \[Beta]) \[Alpha] \[Beta] + \[Sigma]^2 -
E^(t \[Beta]) \[Sigma]^2))/(2 \[Beta]^2 \[Sigma]^2)) +
1/\[Sigma]^2 (2 x \[Beta] ((
E^(-t \[Beta]) (-1 + E^(2 t \[Beta])))/(2 \[Beta])) +
2 x (E^(t \[Beta]) -
1/2 E^(-t \[Beta]) (-1 + E^(2 t \[Beta])) )))},
X3 = {0, 0, u},
X4 = {0, 1, 0}