9.1: Chapter 1 Answers

Section 1.2

1. Third order, nonlinear.

2. Second order, linear.

3. First order, linear.

4. Second order, nonlinear.

5. Third order, linear.

6. Second order, nonlinear.

7. Ordinary, second order

8. Ordinary, third order

9. Partial, first order

10. Ordinary, fourth order

11. Partial, second order

Section 1.3

1. a. \(x_{0}\neq k\pi \;\;\;\;(k=\text{integer})\); all \(y_0\)

b. \(x_{0}\neq k\pi \;\;\;\;(k=\text{integer})\); all \(y_0\)

2. a. all \((x_0,y_0)\) except for \((0,0) \)

b. all \((x_0,y_0)\) except for \((0,0) \)

3. a. \(x_{0}y_{0}\neq (2k+1)\frac{\pi }{2} \;\;\;\; (k=\text{integer})\)

b. \(x_{0}y_{0}\neq (2k+1)\frac{\pi }{2} \;\;\;\; (k=\text{integer})\)

4. a. \(x_{0}y_{0}>0\text{ and }x_{0}y_{0}\neq 1\)

b. \(x_{0}y_{0}>0\text{ and }x_{0}y_{0}\neq 1\)

5. a. all \((x_{0},y_{0})\)

b. \((x_{0},y_{0})\) with \(y_{0}\neq 0\)

6. a. all \((x_{0}, y_{0})\)

b. all \((x_{0}, y_{0})\)

7. a. all \((x_{0}, y_{0})\)

b. all \((x_{0}, y_{0})\)

8. a. \((x_{0}, y_{0})\) such that \(x_{0}\neq 4y_{0}\)

b. \((x_{0}, y_{0})\) such that \(x_{0}\neq 4y_{0}\)

9. a. all \((x_{0}, y_{0})\)

b. all \((x_{0}, y_{0})\) with \(y_{0}\neq\pm 1\)

11. a. all \((x_{0}, y_{0})\)

b. all \((x_{0}, y_{0})\)

12. a. all \((x_{0}, y_{0})\) such that \(y_0 > -x_0\)

b. all \((x_{0}, y_{0})\) such that \(y_0 > -x_0\)

13. a. all \((x_{0}, y_{0})\) with \(x_{0}\neq 1,\quad y_{0}\neq (2k+1)\frac{\pi }{2}(k=\text{integer})\)

b. all \((x_{0}, y_{0})\) with \(x_{0}\neq 1,\quad y_{0}\neq (2k+1)\frac{\pi }{2}(k=\text{integer})\)