A.5.2: Section 5.2 Answers
- Page ID
- 43766
1. \(y=c_{1}e^{-6x}+c_{2}e^{x}\)
2. \(y=e^{2x}(c_{1}\cos x+c_{2}\sin x)\)
3. \(y=c_{1}e^{-7x}+c_{2}e^{-x}\)
4. \(y=e^{2x}(c_{1}+c_{2}x)\)
5. \(y=e^{-x}(c_{1}\cos 3x+c_{2}\sin 3x)\)
6. \(y=e^{-3x}(c_{1}\cos x+c_{2}\sin x)\)
7. \(y=e^{4x}(c_{1}+c_{2}x)\)
8. \(y=c_{1}+c_{2}e^{-x}\)
9. \(y=e^{x}(c_{1}\cos\sqrt{2}x+c_{2}\sin\sqrt{2}x)\)
10. \(y=e^{-3x}(c_{1}\cos 2x+c_{2}\sin 2x)\)
11. \(y=e^{-x/2}\left(c_{1}\cos\frac{3x}{2}+c_{2}\sin\frac{3x}{2} \right)\)
12. \(y=c_{1}e^{-x/5}+c_{2}e^{x/2}\)
13. \(y = e ^{-7x} (2 \cos x − 3 \sin x)\)
14. \(y=4e^{x/2}+6e^{-x/3}\)
15. \(y=3e^{x/3}-4e^{-x/2}\)
16. \(y=\frac{e^{-x/2}}{3}+\frac{3e^{3x/2}}{4}\)
17. \(y=e^{3x/2}(3-2x)\)
18. \(y=3^{-4x}-4e^{-3x}\)
19. \(y=2xe^{3x}\)
20. \(y=e^{x/6}(3+2x)\)
21. \(y=e^{-2x}\left(3\cos\sqrt{6}x+\frac{2\sqrt{6}}{3}\sin\sqrt{6}x \right)\)
23. \(y=2e^{-(x-1)}-3e^{-2(x-1)}\)
24. \(y=\frac{1}{3}e^{-(x-2)}-\frac{2}{3}e^{7(x-2)}\)
25. \(y=e^{7(x-1)}(2-3(x-1))\)
26. \(y=e^{-(x-2)/3}(2-4(x-2))\)
27. \(y=2\cos\frac{2}{3}\left(x-\frac{\pi }{4} \right) -3\sin\frac{2}{3}\left(x-\frac{\pi }{4} \right)\)
28. \(y=2\cos\sqrt{3}\left( x-\frac{\pi }{3}\right)-\frac{1}{\sqrt{3}}\sin\sqrt{3}\left(x-\frac{\pi }{3} \right)\)
30. \(y=\frac{k_{0}}{r_{2}-r_{1}}\left(r_{2}e^{r_{1}(x-x_{0})}-r_{1}e^{r_{2}(x-x_{0})} \right) +\frac{k_{1}}{r_{2}-r_{1}}\left(e^{r_{2}(x-x_{0})}-e^{r_{1}(x-x_{0})} \right)\)
31. \(y=e^{r_{1}(x-x_{0})}[k_{0}+(k_{1}-r_{1}k_{0})(x-x_{0})]\)
32. \(y=e^{\lambda (x-x_{0})}\left[ k_{0}\cos\omega (x-x_{0})+\left(\frac{k_{1}-\lambda k_{0}}{\omega } \right)\sin\omega (x-x_{0}) \right]\)