In 1922, match an equation with the slope field. (a) y = 0.05y(10 y) (b) y = 0.05x(10 x)

(a) For dy/dx = x2y2, find the slope at the following points: (1, 0), (0, 1), (1, 1), (2, 1), (1, 2), (2, 2) (b) Sketch the slope field at these points.

Sketch the slope field for dy/dx = x/y at the points marked in Figure 11.14.

Sketch the slope field for dy/dx = y2 at the points marked in Figure 11.15.

Match each of the slope field segments in (I)(VI) with one or more of the differential equations in (a)(f). (a) y = ex2 (b) y = cos y (c) y = cos(4 y) (d) y = y(4 y) (e) y = y(3 y) (f) y = x(3 x)

Sketch three solution curves for each of the slope fields in Figures 11.16 and 11.17.

Sketch three solution curves for each of the slope fields in Figure 11.18.

One of the slope fields in Figure 11.18 is the slope field for y = x2 y2. Which one? On this field, where is the point (0, 1)? The point (1, 0)? (Assume that the x and y scales are the same.) Sketch the line x = 1 and the solution curve passing through (0, 1) until it crosses x = 1.

The slope field for the equation y = x(y 1) is shown in Figure 11.19. (a) Sketch the solutions that pass through the points (i) (0, 1) (ii) (0, 1) (iii) (0, 0) (b) From your sketch, write down the equation of the solution with y(0) = 1. (c) Check your solution to part (b) by substituting it into the differential equation.

The slope field for the equation y = x + y is shown in Figure 11.20. (a) Sketch the solutions that pass through the points (i) (0, 0) (ii) (3, 1) (iii) (1, 0) (b) From your sketch, write the equation of the solution passing through (1, 0). (c) Check your solution to part (b) by substituting it into the differential equation.

Sketch a slope field with the following properties. (Draw at least ten line segments, including some with x < 0, with x > 0, and with x = 0.) dy dx > 0 for x < 0, dy dx < 0 for x > 0, dy dx = 0 for x = 0.

Sketch a slope field with the following properties. (Draw at least ten line segments, including some with P < 2, with 2

(a) Sketch the slope field for the equation y = x y in Figure 11.21 at the points indicated. (b) Find the equation for the solution that passes through the point (1, 0) .

The slope field for the equation dP/dt = 0.1P(10P), for P 0, is in Figure 11.22. (a) Sketch the solutions that pass through the points (i) (0, 0) (ii) (1, 4) (iii) (4, 1) (iv) (5, 1) (v) (2, 12) (vi) (2, 10) (b) For which positive values of P are the solutions increasing? Decreasing? If P(0) = 5, what is the limiting value of P as t gets large

The slope field for y = 0.5(1 + y)(2 y) is shown in Figure 11.23. (a) Plot the following points on the slope field: (i) the origin (ii) (0, 1) (iii) (1, 0) (iv) (0, 1) (v) (0, 5/2) (vi) (0, 5/2) (b) Plot solution curves through the points in part (a). (c) For which regions are all solution curves increasing? For which regions are all solution curves decreasing? When can the solution curves have horizontal tangents? Explain why, using both the slope field and the differential equation.

One of the slope fields in Figure 11.24 is the slope field for y = (x + y)/(x y). Which one?

The slope field for y = (sin x)(sin y) is in Figure 11.25. (a) Sketch the solutions that pass through the points (i) (0, 2) (ii) (0, ) (b) What is the equation of the solution that passes through (0, n), where n is any integer?

Match the slope fields in Figure 11.26 with their differential equations. Explain your reasoning. (a) y = y (b) y = y (c) y = x (d) y = 1/y (e) y = y2

Match the slope fields in Figure 11.27 to the corresponding differential equations: (a) y = xex (b) y = sin x (c) y = cos x (d) y = x2ex (e) y = ex2 (f) y =

In Problems 1922, match an equation with the slope field. (a) y = 0.05y(10 y) (b) y = 0.05x(10 x) (c) y = 0.05y(5 y) (d) y = 0.05x(5 x) (e) y = 0.05y(y 10) (f) y = 0.05x(x 10) (g) y = 0.05y(y 5) (h) y = 0.05x(x 5) (i) y = 0.05x(y 5)

In Problems 1922, match an equation with the slope field. (a) y = 0.05y(10 y) (b) y = 0.05x(10 x) (c) y = 0.05y(5 y) (d) y = 0.05x(5 x) (e) y = 0.05y(y 10) (f) y = 0.05x(x 10) (g) y = 0.05y(y 5) (h) y = 0.05x(x 5) (i) y = 0.05x(y 5)

In Problems 1922, match an equation with the slope field. (a) y = 0.05y(10 y) (b) y = 0.05x(10 x) (c) y = 0.05y(5 y) (d) y = 0.05x(5 x) (e) y = 0.05y(y 10) (f) y = 0.05x(x 10) (g) y = 0.05y(y 5) (h) y = 0.05x(x 5) (i) y = 0.05x(y 5)

In Problems 1922, match an equation with the slope field. (a) y = 0.05y(10 y) (b) y = 0.05x(10 x) (c) y = 0.05y(5 y) (d) y = 0.05x(5 x) (e) y = 0.05y(y 10) (f) y = 0.05x(x 10) (g) y = 0.05y(y 5) (h) y = 0.05x(x 5) (i) y = 0.05x(y 5)

Match the following differential equations with the slope fields shown in Figure 11.28. Explain your reasoning. (a) dy dx = e x2 (b) dy dx = e2x2 (c) dy dx = ex2/2 (d) dy dx = e0.5x cos x (e) dy dx = 1 (1 + 0.5 cos x)2 (f) dy dx = ex2 x (I) y

The Gompertz equation, which models growth of animal tumors, is y = ay ln(y/b), where a and b are positive constants. Use Figures 11.29 and 11.30 to write a paragraph describing the similarities and/or differences between solutions to the Gompertz equation with a = 1 and b = 2 and solutions to the equation y = y(2 y).

There is a differential equation that has y = x as one of its solutions and a slope field with a slope of 0 at the point (1, 1).

Figure 11.31 shows the slope field of y = y

Figure 11.31 shows the slope field of y = y

A differential equation that has a slope field with all the slopes above the x-axis positive and all the slopes below the x-axis negative

A slope field for a differential equation where the formula for dy/dx depends on x but not y.

A slope field for a differential equation where the formula for dy/dx depends on y but not x.

All solutions to the differential equation whose slope field is in Figure 11.32 have limx y = .

All solutions to the differential equation whose slope field is in Figure 11.33 have limx y = 0.

All solutions to the differential equation whose slope field is in

The solutions of the differential equation dy/dx = x2 + y2 + 1 are increasing at every point

The solutions of the differential equation dy/dx = x2 + y2 + 1 are concave up at every point.

In Problems 3644, decide whether the statement is true or false. Assume that y = f(x) is a solution to the equation dy/dx = 2x y. Justify your answer

In Problems 3644, decide whether the statement is true or false. Assume that y = f(x) is a solution to the equation dy/dx = 2x y. Justify your answer

In Problems 3644, decide whether the statement is true or false. Assume that y = f(x) is a solution to the equation dy/dx = 2x y. Justify your answer

In Problems 3644, decide whether the statement is true or false. Assume that y = f(x) is a solution to the equation dy/dx = 2x y. Justify your answer

In Problems 3644, decide whether the statement is true or false. Assume that y = f(x) is a solution to the equation dy/dx = 2x y. Justify your answer

In Problems 3644, decide whether the statement is true or false. Assume that y = f(x) is a solution to the equation dy/dx = 2x y. Justify your answer

In Problems 3644, decide whether the statement is true or false. Assume that y = f(x) is a solution to the equation dy/dx = 2x y. Justify your answer

In Problems 3644, decide whether the statement is true or false. Assume that y = f(x) is a solution to the equation dy/dx = 2x y. Justify your answer

In Problems 3644, decide whether the statement is true or false. Assume that y = f(x) is a solution to the equation dy/dx = 2x y. Justify your answer