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## Homework Statement

use the greens function G(x,z) to solve inhomogeneous problem:

(1-x

^{2}) 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-x

^{2})

^{1/2}(1-z

^{2})

^{1/2}

## The Attempt at a Solution

the general solution to the equation

(1-x

^{2}) y'' - x y' + y = 0

is:

y = Ax + B(1-x

^{2})

^{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-x

^{2})

^{1/2}

then i did this:

-D(z)x(1-x

^{2})

^{-1/2}- A(z) = 1 *

D(z)(1-x

^{2})

^{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???