- #1
sara_87
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Homework Statement
use the greens function G(x,z) to solve inhomogeneous problem:
(1-x2 ) y'' - x y' + y = f(x)
y(0) = y(1) = 0
Homework Equations
the answer is:
G(x,z)= -x for x<z
and -z(1-x2 ) 1/2 (1-z2 ) 1/2
The Attempt at a Solution
the general solution to the equation
(1-x2 ) y'' - x y' + y = 0
is:
y = Ax + B(1-x2 ) 1/2
i found B(z) and D(z) = 0 after subing in x= 1 and x= 0
then i got:
G(x,z) = A(z)
and D(z)(1-x2 )1/2
then i did this:
-D(z)x(1-x2) -1/2 - A(z) = 1 *
D(z)(1-x2) 1/2 - A(z)x = 0 **
now we have 2 equation with 2 unknown which i can solve... but i didn't get the right answer so i just need to check are the 2 equations * and ** correct?