Consider the ODE y"-k²y = f(x) 0≤x≤1 k > 0 with boundary conditions (a) (b) y(0) = 0 y(1) = 0 Compute the Green's function G(x, x') for this ODE. That is, solve the boundary value problem d²G - k²G(x, x') = d(x − x') dx2 with boundary conditions G(x = 0, x) = 0 G(x = 1, x') = 0 and where 8(x) is the delta function. Use the Green's function developed in part (a) to solve the inhomo- geneous boundary value problem = y"-k²y 10≤ x ≤1 k > 0 with boundary conditions y(0) = 0 y(1) = 0 You may leave your answer in terms of integrals.
Consider the ODE y"-k²y = f(x) 0≤x≤1 k > 0 with boundary conditions (a) (b) y(0) = 0 y(1) = 0 Compute the Green's function G(x, x') for this ODE. That is, solve the boundary value problem d²G - k²G(x, x') = d(x − x') dx2 with boundary conditions G(x = 0, x) = 0 G(x = 1, x') = 0 and where 8(x) is the delta function. Use the Green's function developed in part (a) to solve the inhomo- geneous boundary value problem = y"-k²y 10≤ x ≤1 k > 0 with boundary conditions y(0) = 0 y(1) = 0 You may leave your answer in terms of integrals.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...
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help me with part B please. pelase handwrite detailed solution; do not use AI tools or typing. Because sometimes typing formula is difficult to see. Please make the formula look clear. Thanks
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