Differential Equations and Linear Algebra, 4th Edition

Section 1.2

1. 1. $y(x)=x^2+x+3$

2. 2. $y(x)=\frac{1}{3}{\left(x-2\right)}^3+1$

3. 3. $y(x)=\frac{1}{3}\left(2x^{\mathrm{3/2}}-16\right)$

4. 4. $y(x)=-1/x+6$

5. 5. $y(x)=2\sqrt{x+2}-5$

6. 6. $y(x)=\frac{1}{3}\left[{\left(x^2+9\right)}^{\mathrm{3/2}}-125\right]$

7. 7. $y(x)=10{\tan }^{-1}x$

8. 8. $y(x)=\frac{1}{2}\sin 2x+1$

9. 9. $y(x)={\sin }^{-1}x$

10. 10. $y(x)=-\left(x+1\right)e^{-x}+2$

11. 11. $x\left(t\right)=25t^2+10t+20$

12. 12. $x\left(t\right)=-10t^2-15t+5$

13. 13. $x\left(t\right)=\frac{1}{2}{t}^3+5t$

14. 14. $x\left(t\right)=\frac{1}{3}{t}^3+\frac{1}{2}{t}^2-7t+4$

15. 15. $x(t)=\frac{1}{3}{(t+3)}^4-37t-26$

16. 16. $x(t)=\frac{4}{3}{(t+4)}^{\mathrm{3/2}}-5t-\frac{29}{3}$

17. 17. $x(t)=\frac{1}{2}[{(t+1)}^{-1}+t-1]$

18. 19. $x\left(t\right)=\{\begin{array}{ll}5t\hfill & \text{if }0\le t\le \mathrm{5,}\hfill \\ 10t-\frac{1}{2}{t}^2-\frac{25}{2}\hfill & \text{if }5\le t\le 10.\hfill \end{array}$

    

19. 20. $x\left(t\right)=\{\begin{array}{ll}\frac{1}{2}{t}^2\hfill & \text{if }0\le t\le \mathrm{5,}\hfill \\ 5t-\frac{25}{2}\hfill & \text{if }5\le t\le 10.\hfill \end{array}$

    

20. 21. $x\left(t\right)=\{\begin{array}{ll}\frac{1}{2}{t}^2\hfill & \text{if }0\le t\le 5,\hfill \\ 10t-\frac{1}{2}{t}^2-25\hfill & \text{if }5\le t\le 10.\hfill \end{array}$

21. 22. $x\left(t\right)=\{\begin{array}{ll}\frac{5}{6}{t}^2\hfill & \text{if }0\le t\le 3,\hfill \\ 5t-\frac{15}{2}\hfill & \text{if }3\le t\le 7,\hfill \\ \frac{1}{6}\left(-5t^2+100t-290\right)\hfill & \text{if ...}\hfill \end{array}$