

2. $$y=2x^{2}-3x^{3}+\frac{1}{x}$$

3. $$y=2e^{x}+3e^{-x}-e^{2x}+e^{-3x}$$

4. $$y_{i}=\frac{(x-x_{0})^{i-1}}{(i-1)!},\quad 1\leq i\leq n$$

5.

b. $$y_{1}=-\frac{1}{2}x^{3}+x^{2}+\frac{1}{2x},\quad y_{2}=\frac{1}{3}x^{2}-\frac{1}{3x},\quad y_{3}=\frac{1}{4}x^{3}-\frac{1}{3}x^{2}+\frac{1}{12x}$$

c. $$y=k_{0}y_{1}+k_{1}y_{2}+k_{2}y_{3}$$

7. $$2e^{-x^{2}}$$

8. $$\sqrt{2}K\cos x$$

9.

a. $$W(x)=2e^{3x}$$

d. $$y=e^{x}(c_{1}+c_{2}x+c_{3}x^{2})$$

10.

1. $$2$$
2. $$-e^{3x}$$
3. $$4$$
4. $$4/x^{2}$$
5. $$1$$
6. $$2x$$
7. $$2/x^{2}$$
8. $$e^{x}(x^{2}-2x+2)$$
9. $$-240/x^{5}$$
10. $$6e^{2x}(2x-1)$$
11. $$-128x$$

24.

1. $$y'''=0$$
2. $$xy'''-y''-xy'+y=0$$
3. $$(2x-3)y'''-2y''-(2x-5)y'=0$$
4. $$(x^{2}-2x+2)y'''-x^{2}y''+2xy'-2y=0$$
5. $$x^{3}y'''+x^{2}y''-2xy'+2y=9$$
6. $$(3x-1)y'''-(12x-1)y''+9(x+1)y'-9y=0$$
7. $$x^{4}y^{(4)}+5x^{3}y'''-3x^{2}y''-6xy'+6y=0$$
8. $$x^{4}y^{(4)}+3x^{2}y'''-x^{2}y''+2xy'-2y=0$$
9. $$(2x-1)y^{(4)}-4xy'''+(5-2x)y''+4xy'-4y=0$$
10. $$xy^{(4)}-y'''-4xy''+4y'=0$$