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
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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Question
4.1.2.1. Ordinary
![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->](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d6d6ec3-8d2a-4662-b20e-640089acaa34%2F4e2468e1-c6c0-44b8-883a-8c8fcd212c26%2Fifhkia_processed.png&w=3840&q=75)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d6d6ec3-8d2a-4662-b20e-640089acaa34%2F4e2468e1-c6c0-44b8-883a-8c8fcd212c26%2F6t60og9_processed.png&w=3840&q=75)
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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