1. \(y=e^{-ax}\)
2. \(y=ce^{-x^{3}}\)
3. \(y=ce^{-(\ln x)^{2}/2 }\)
4. \(y=\frac{c}{x^{3}}\)
5. \(y=ce^{1/x}\)
6. \(y=\frac{e^{-(x-1)}}{x}\)
7. \(y=\frac{e}{x\ln x}\)
8. \(y=\frac{\pi }{x\sin x}\)
9. \(y=2(1+x^{2})\)
10. \(y=3x^{-k}\)
11. \(y=2(\cos kx)^{1/k}\)
12. \(y=\frac{1}{3}+ce^{-3x}\)
13. \(y=\frac{2}{x}+\frac{c}{x}e^{x}\)
14. \(y=e^{-x^{2}}\left(\frac{x^{2}}{2}+c \right)\)
15. \(y=-\frac{e^{-x}+c}{1+x^{2}}\)
16. \(\frac{7\ln |x|}{x}+\frac{3}{2}x+\frac{c}{x}\)
17. \(y=(x-1)^{-4}(\ln |x-1|-\cos x+c)\)
18. \(y=e^{-x^{2}}\left(\frac{x^{3}}{4}+\frac{c}{x} \right)\)
19. \(y=\frac{2\ln |x|}{x^{2}}+\frac{1}{2}+\frac{c}{x^{2}}\)
20. \(y=(x+c)\cos x\)
21. \(y=\frac{c-\cos x}{(1+x)^{2}}\)
22. \(y=-\frac{1}{2}\frac{(x-2)^{3}}{(x-1)}+c\frac{(x-2)^{5}}{(x-1)}\)
23. \(y=(x+c)e^{-\sin ^{2}x}\)
24. \(y=\frac{e^{x}}{x^{2}}-\frac{e^{x}}{x^{3}}+\frac{c}{x^{2}}\)
25. \(y=\frac{e^{3x}-e^{-7x}}{10}\)
26. \(y=\frac{2x+1}{(1+x^{2})^{2}}\)
27. \(y=\frac{1}{x^{3}}\ln \left(\frac{1+x^{2}}{2} \right)\)
28. \(y=\frac{1}{2}(\sin x +\csc x)\)
29. \(y=\frac{2\ln |x|}{x}+\frac{x}{2}-\frac{1}{2x}\)
30. \(y=(x-1)^{-3}[\ln (1-x)-\cos x]\)
31. \(y=2x^{2}+\frac{1}{x^{2}}\quad (0,\infty )\)
32. \(y=x^{2}(1-\ln x)\)
33. \(y=\frac{1}{2}+\frac{5}{2}e^{-x^{2}}\)
34. \(y=\frac{\ln |x-1|+\tan x+1}{(x-1)^{3}}\)
35. \(y=\frac{\ln |x|+x^{2}+1}{(x+2)^{4}}\)
36. \(y=(x^{2}-1)\left(\frac{1}{2}\ln |x^{2}-1|-4 \right)\)
37. \(y=-(x^{2}-5)(7+\ln |x^{2}-5|)\)
38. \(y=e^{-x^{2}}\left(3+\int _{0}^{x} t^{2}e^{t^{2}}dt \right)\)
39. \(y=\frac{1}{x}\left(2+\int_{1}^{x}\frac{\sin t}{t}dt \right)\)
40. \(y=e^{-x}\int_{1}^{x}\frac{\tan t}{t}dt\)
41. \(y=\frac{1}{1+x^{2}}\left(1+\int_{0}^{x}\frac{e^{t}}{1+t^{2}}dt \right)\)
42. \(y=\frac{1}{x}\left( 2e^{-(x-1)}+e^{-x}\int_{1}^{x}e^{t}e^{t^{2}}dt \right)\)
43. \(G=\frac{r}{\lambda }+\left( G_{0}-\frac{r}{\lambda} \right)e^{-\lambda t}\lim _{t\to\infty}G(t)=\frac{r}{\lambda}\)
45. \(y=y_{0}e^{-a(x-x_{0})}+e^{-ax}\int_{x_{0}}^{x}e^{at}f(t)dt\)
48.
- \(y=\tan ^{-1}\left(\frac{1}{3}+ce^{3x} \right) \)
- \(y=\pm\left[\ln\left(\frac{1}{x}+\frac{c}{x^{2}} \right) \right]^{1/2}\)
- \(y=\text{exp}\left(x^{2}+\frac{c}{x^{2}} \right)\)
- \(y=-1+\frac{x}{c+3\ln |x|}\)
