The eigenfunctions for y"-2y' + Xy = 0,y(0) = 1, y(1) = 0 areO {e I sin(-TLAI2.Sn-1O {e* sin(")}n 1TLAI2O {e² sin(nax)}, 100O {e 2" sin(naz)}100O {e 2" sin(")}O {e "sin(nTI)},1O {e2" sin2O {e sin(nnz)}

Answered: Image /qna-images/answer/68f24c61-3254-46ce-ae2d-6dfb5429006b.jpg

The eigenfunctions for y"-2y + Ay = 0, y(0) = 1, y(1) = 0 are O {e I sin ()}, n-1 O {e² sin(")}, TLTI 00 O {e* sin(nrz)} 1 00 O {e 2* 00 sin(nn2)},1 O {e 2# sin()}, 100 Sn 1 SI O {e "sin(nrz)} 1 O {e2" sin( )} O {e2" sin(nnr)},"

The eigenfunctions for y"-2y + Ay = 0, y(0) = 1, y(1) = 0 are O {e I sin ()}, n-1 O {e² sin(")}, TLTI 00 O {e* sin(nrz)} 1 00 O {e 2* 00 sin(nn2)},1 O {e 2# sin()}, 100 Sn 1 SI O {e "sin(nrz)} 1 O {e2" sin( )} O {e2" sin(nnr)},"

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

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 10E

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Question

The eigenfunctions for y"-2y' + Xy = 0,
y(0) = 1, y(1) = 0 are
O {e I sin(-
TLAI
2.
Sn-1
O {e* sin(")}n 1
TLAI
2
O {e² sin(nax)}, 1
00
O {e 2" sin(naz)}1
00
O {e 2" sin(")}
O {e "sin(nTI)},1
O {e2" sin
2
O {e sin(nnz)}

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