logistic_guy
Senior Member
- Joined
- Apr 17, 2024
- Messages
- 1,308
Solve the differential equation by Dirac delta function to obtain Green's function.
dx2d2y+k2y=f(x)
a<x<b
dx2d2y+k2y=f(x)
a<x<b
This should be written as:g(x,s)=⎩⎪⎪⎨⎪⎪⎧sink(x−a)sink(b−x)a≤s<xx<s≤b
A and B in this system are in fact not constants. They are functions of x. Therefore, they should be written as A(x) and B(x). I wrote them without the variable x, just to save some ink and also the system looks more clean like this!g(x,s)=⎩⎪⎪⎨⎪⎪⎧Asink(s−a)Bsink(b−s)a≤s<xx<s≤b
Let us solve for A in the first equation.Asink(x−a)−Bsink(b−x)=0
−kBcosk(b−x)−kAcosk(x−a)=1