Suppose the solution of the boundary-value problem y Py Qy
Chapter 4, Problem 4.1.383(choose chapter or problem)
Suppose the solution of the boundary-value problem y Py Qy f(x), y(a) 0, y(b) 0, x2 is given by where and are solutions of the associated homogeneous differential equation chosen in the construction of so that and Prove that the solution of the boundary-value problem with nonhomogeneous DE and boundary conditions, is given by y(x) yp(x) B y1(b) y1(x) A y2(a) y2(x). y Py Qy f(x), y(a) A, y(b) B y2 y (b) 0. 1(a) 0 G(x, t) y2(x) y1 y (x) p(x) b a b, aG(x, t)f(t)dt [Hint: In your proof, you will have to show that Reread the assumptions following (24).]
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