If A,=3and A2 =2are the eigenvalues of2y(x) =1 (xt+x?²) y(t) dtwith corresponding orthonormal eigenfunctionsV109,(x) =-x, and p,(x) =x?.2Then, the IE,y(x) = x? +1+ (xt+x?) y(1) dt, hasUnique solutionInfinitely many solutionsNo solution

First Using orthogonal of two function by integrating. Second image by contradiction assuming there…

3 If A, and A2 = 2 are the eigenvalues of 2 y(x) =1 (xt+x?²) y(t) dt with corresponding orthonormal eigenfunctions V10 x, and p,(x) = x?. 2 6. 9,(x) = Then, the IE, y(x)= x² +1+S cx+ x?t°) y(1) dt, has 2 Unique solution Infinitely many solutions No solution

3 If A, and A2 = 2 are the eigenvalues of 2 y(x) =1 (xt+x?²) y(t) dt with corresponding orthonormal eigenfunctions V10 x, and p,(x) = x?. 2 6. 9,(x) = Then, the IE, y(x)= x² +1+S cx+ x?t°) y(1) dt, has 2 Unique solution Infinitely many solutions No solution

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.1: Eigenvalues And Eigenvectors

Problem 65E

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Question

If A,=
3
and A2 =
2
are the eigenvalues of
2
y(x) =1 (xt+x?²) y(t) dt
with corresponding orthonormal eigenfunctions
V10
9,(x) =-
x, and p,(x) =
x?.
2
Then, the IE,
y(x) = x? +1+ (xt+x?) y(1) dt, has
Unique solution
Infinitely many solutions
No solution

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