Daniel Farrell's profile - activity

Thank you very much, that's a very clever solution.

reset()
var('I_1 I_2 I0 A B C D c c1 c2 x alpha D')
I_1 = function('I_1', x)
I_2 = function('I_2', x)
eq1 =  diff(I_1,x) == -alpha * I_1
eq2 = -diff(I_2,x) == -alpha * I_2
sol1 = desolve( eq1,I_1,ivar=x)
sol2 = desolve( eq2,I_2,ivar=x)
sol1=sol1.subs(c=c1)
sol2=sol2.subs(c=c2) 
e1=sol1.subs(x=0)==A*sol2.subs(x=0)+C
e2=sol2.subs(x=D)==B*sol1.subs(x=D)
sol=solve([e1,e2],[c1,c2])
print "I_1 =",sol1.subs(sol[0][0])
print "I_2 =",sol2.subs(sol[0][1])

#I_1 = -C*e^(2*D*alpha - alpha*x)/(A*B - e^(2*D*alpha))
#I_2 = -B*C*e^(alpha*x)/(A*B - e^(2*D*alpha))

I am using desolve_system() to solve a boundary value problem. The equations are very simple but I'm having a bit of difficulty trying to include the boundary conditions. The system of equations and boundary conditions are,

This is the code that I'm using in sage. How can I include the boundary values in this problem?

reset()
var('I_1 I_2 I0 R0 R1 x alpha D')
I_1 = function('I_1', x)
I_2 = function('I_2', x)
eq1 =  diff(I_1,x) == -alpha * I_1
eq2 = -diff(I_2,x) == -alpha * I_2
sol = desolve_system( [eq1, eq2], [I_1, I_2], ivar=x)
view(sol)
# How can I include these?
#BV1: I_1(x=0)==A*I_2(x=0) + C
#BV2: I_2(x=D)==B*I_1(x=D)