For the nonhomogeneous linear DE y\"(x) + p1(x)y\'(x) + p2(x) y(x) = g(x), Green

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For the nonhomogeneous linear DE y"(x) + p1(x)y'(x) + p2(x) y(x) = g(x), Green's function yp(x) is defined by where x0 is a fixed point, y1(x),y2(x) are solutions to the homogeneous linear DE, and W(x) is their Wronskian . Show that yp(x) satisfies the condition yp(x0) = 0. Show that yp(x) satisfies the condition yp'(x0) = 0. Hint: Notice yp(x) = y2(x). Show that yp(x) is a solution for the nonhomogeneous liner DE. Let x0 be an arbitary point. Show that the Green's function reduce linear DE. Let x0 be an arbitrary point. Show that the Green's function

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