nagle_differential_equations_ISM_Part61

nagle_differential_equations_ISM_Part61 - Chapter 10 24. u...

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Unformatted text preview: Chapter 10 24. u ( x,y ) = X n =1 A n e- ny sin nx , where A n = 2 Z f ( x ) sin nxdx 296 CHAPTER 11: Eigenvalue Problems and Sturm-Liouville Equations EXERCISES 11.2: Eigenvalues and Eigenfunctions 2. sin x- cos x + x + 1 4. ce- 2 x (sin 2 x + cos 2 x ) 6. 2 e x + e- x- x 8. c 1 sin 2 x + c 2 cos 2 x + 1 10. No solution 12. No solution 14. n = 2 n 2 9 ; y n ( x ) = b n sin nx 3 + c n cos nx 3 , n = 0 , 1 , 2 ,... 16. n = 2 + (2 n + 1) 2 4 ; y n ( x ) = c n sin (2 n + 1) x 2 , n = 0 , 1 , 2 ,... 18. =- 2 , where tanh ( ) = 2 ; y ( x ) = c sinh ( x ); n = 2 n , where tan ( n ) = 2 n ; y n ( x ) = c n sin ( n x ), n = 1 , 2 , 3 ,... 20. n = 2 n 2 , y n ( x ) = c n cos ( n ln x ), n = 0 , 1 , 2 ,... 22. 1 = 4 . 116 , 2 = 24 . 139 , 3 = 63 . 659 24. No nontrivial solutions 26. n = 2 n , where cot ( n ) = n for n > 0; y n ( x ) = c n sin ( n x ), n = 1 , 2 , 3 ,......
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This note was uploaded on 02/12/2011 for the course MA 221 taught by Professor Mazmani during the Spring '08 term at Stevens.

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nagle_differential_equations_ISM_Part61 - Chapter 10 24. u...

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