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In this problem we find the eigenfunctions and eigenvalues of the differential equation d²y dx² on the interval 0 ≤ x ≤ a, where a > 0, with boundary values y(0) = 0 y(a) = 0. For the general solution of the differential equation in the following cases use A and B for your constants, for example y = A cos(x) + Bsin(x). For the variable A type the word lambda, otherwise treat it as you would any other variable. Case 1: X=0 + Ay = 0 (1a.) (Fill all three answer blanks to receive credit.) Ignoring the boundary values for a moment, the general solution of differential equation is y(x) = Apply the boundary conditions to the general solution to obtain two equations relating A to B: (1b.) Solving for A and B we obtain A = B = = 0 = 0 ✔

In this problem we find the eigenfunctions and eigenvalues of the differential equation d²y dx² on the interval 0 ≤ x ≤ a, where a > 0, with boundary values y(0) = 0 y(a) = 0. For the general solution of the differential equation in the following cases use A and B for your constants, for example y = A cos(x) + Bsin(x). For the variable A type the word lambda, otherwise treat it as you would any other variable. Case 1: X=0 + Ay = 0 (1a.) (Fill all three answer blanks to receive credit.) Ignoring the boundary values for a moment, the general solution of differential equation is y(x) = Apply the boundary conditions to the general solution to obtain two equations relating A to B: (1b.) Solving for A and B we obtain A = B = = 0 = 0 ✔

Calculus For The Life Sciences
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.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 34CR
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4.1.2.1. Ordinary Differential Equation 

In this problem we find the eigenfunctions and eigenvalues of the differential equation d²y dx² on the interval 0 ≤ x ≤ a, where a > 0, with boundary values y(0) = 0 y(a) = 0. your For the general solution of the differential equation in the following cases use A and B for constants, for example y A cos(x) + B sin(x). For the variable A type the word lambda, otherwise treat it as you would any other variable. Case 1: 0 = (1a.) (Fill all three answer blanks to receive credit.) Ignoring the boundary values for a moment, the general solution of differential equation is + xy = 0 y(x) Apply the boundary conditions to the general solution to obtain two equations relating A to B: (1b.) Solving for A and B we obtain = A = B = ▶ = 0 = 0 1->
Transcribed Image Text:In this problem we find the eigenfunctions and eigenvalues of the differential equation d²y dx² on the interval 0 ≤ x ≤ a, where a > 0, with boundary values y(0) = 0 y(a) = 0. your For the general solution of the differential equation in the following cases use A and B for constants, for example y A cos(x) + B sin(x). For the variable A type the word lambda, otherwise treat it as you would any other variable. Case 1: 0 = (1a.) (Fill all three answer blanks to receive credit.) Ignoring the boundary values for a moment, the general solution of differential equation is + xy = 0 y(x) Apply the boundary conditions to the general solution to obtain two equations relating A to B: (1b.) Solving for A and B we obtain = A = B = ▶ = 0 = 0 1->
Case 2: <0 (2a.) (Fill all three answer blanks to receive credit.) Ignoring the boundary values for a moment, the general solution of differential equation is y(x) = Apply the boundary conditions to obtain equations relating A to B: 0 (2b.) Since A, a ‡ 0, the only solution of these equations is A = B = J = = 0 ← J
Transcribed Image Text:Case 2: <0 (2a.) (Fill all three answer blanks to receive credit.) Ignoring the boundary values for a moment, the general solution of differential equation is y(x) = Apply the boundary conditions to obtain equations relating A to B: 0 (2b.) Since A, a ‡ 0, the only solution of these equations is A = B = J = = 0 ← J
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Calculus For The Life Sciences
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