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11.9: A.11.1- Section 11.1 Answers

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Dec 31, 2022
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- 11.8: A.10.7- Section 10.7 Answers
- 11.10: A.11.2- Section 11.2 Answers

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2. $\lambda_{n}=n^{2},\quad y_{n}=\sin nx,\quad n=1,2,3,\ldots$

3. $\lambda_{0}=0,\quad y_{0}=1;\quad \lambda_{n}=n^{2},\quad y_{n}=\cos nx,\quad n=1,2,3,\ldots$

4. $\lambda_{n}=\frac{(2n-1)^{2}}{4},\quad y_{n}=\sin\frac{(2n-1)x}{2},\quad n=1,2,3,\ldots$

5. $\lambda_{n}=\frac{(2n-1)^{2}}{4},\quad y_{n}=\cos\frac{(2n-1)x}{2},\quad n=1,2,3,\ldots$

6. $\lambda_{0},\quad y_{0}=1,\quad \lambda_{n}=n^{2},\quad y_{1n}=\cos nx,\quad y_{2n}=\sin nx,\quad n=1,2,3,\ldots$

7. $\lambda_{n}=n^{2}\pi ^{2},\quad y_{n}=\cos n\pi x,\quad n=1,2,3,\ldots$

8. $\lambda_{n}=\frac{(2n-1)^{2}\pi ^{2}}{4},\quad y_{n}=\cos\frac{(2n-1)\pi x}{2},\quad n=1,2,3,\ldots$

9. $\lambda_{n}=n^{2}\pi ^{2},\quad y_{n}=\sin n\pi x,\quad n=1,2,3,\ldots$

10. $\lambda_{0}=0,\quad y_{0}=1,\quad \lambda_{n}=n^{2}\pi ^{2},\quad y_{1n}=\cos n\pi x,\quad y_{2n}=\sin n\pi xn\quad n=1,2,3,\ldots$

11. $\lambda_{n}=\frac{(2n-1)^{2}\pi ^{2}}{4},\quad y_{n}=\sin\frac{(2n-1)\pi x}{2},\quad n=1,2,3,\ldots$

12. $\lambda_{0},\quad y_{0}=1,\quad \lambda_{n}=\frac{n^{2}\pi ^{2}}{4},\quad y_{1n}=\cos\frac{n\pi x}{2},\quad y_{2n}=\sin\frac{n\pi x}{2},\quad n=1,2,3,\ldots$

13. $\lambda_{n}=\frac{n^{2}\pi ^{2}}{4},\quad y_{n}=\sin\frac{n\pi x}{2},\quad n=1,2,3,\ldots$

14. $\lambda_{n}=\frac{(2n-1)^{2}\pi ^{2}}{36},\quad y_{n}=\cos\frac{(2n-1)\pi x}{6},\quad n=1,2,3,\ldots$

15. $\lambda_{n}=(2n-1)^{2}\pi ^{2},\quad y_{n}=\sin (2n-1)\pi x,\quad n=1,2,3,\ldots$

16. $\lambda_{n}=\frac{n^{2}\pi ^{2}}{25},\quad y_{n}=\cos\frac{n\pi x}{5},\quad n=1,2,3,\ldots$

23. $\lambda_{n}=4n^{2}\pi ^{2}/L^{2}\quad y_{n}=\sin\frac{2n\pi x}{L},\quad n=1,2,3,\ldots$

24. $\lambda_{n}=n^{2}\pi ^{2}/L^{2}\quad y_{n}=\cos\frac{n\pi x}{L},\quad n=1,2,3,\ldots$

25. $\lambda_{n}=4n^{2}\pi ^{2}/L^{2}\quad y_{n}=\sin\frac{2n\pi x}{L},\quad n=1,2,3,\ldots$

26. $\lambda_{n}=n^{2}\pi ^{2}/L^{2}\quad y_{n}=\cos\frac{n\pi x}{L},\quad n=1,2,3,\ldots$

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