The graph of the function f(r) is (1 point) (the horizontal axis is x.) Given the differential equation z'(t) = f(z(t)). List the constant (or equilibrium) solutions to this differential equation in increasing order and indicate whether or not these equations are stable, semi-stable, or unstable
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We were unable to transcribe this imageThe graph of the function f(r) is (1 point) (the horizontal axis is x.) Given the differential equation z'(t) = f(z(t)). List the constant (or equilibrium)...
The graph of the function f(x) is, and the the horizontal axis is x. Given the...
The graph of the function f(x) is, and the the
horizontal axis is x.
Given the differential equation
x?(t)=f(x(t))x?(t)=f(x(t)).
List the constant (or equilibrium) solutions to this differential
equation in increasing order and indicate whether or not these
equations are stable, semi-stable, or unstable. (The second line
after the comma has a drop menu that asks for stable, semi-stable,
or unstable.)
A.) ________ , ________
B.) ________ , ________
C.) ________ , ________
D.) ________ , ________
4 Consider the autonomous differential equation y f(v) a) (3 points) Find all the equilibrium solutions (critical...
4 Consider the autonomous differential equation y f(v) a) (3 points) Find all the equilibrium solutions (critical points). b) (3 points) Use the sign of y f(z) to determine where solutions are increasing / decreasing. Sketch several solution curves in each region determined by the critical points in c) (3 points) the ty-plane. d) (3 points) Classify each equilibrium point as asymptotically stable, unstable, or semi-stable and draw the corresponding phase line.
4 Consider the autonomous differential equation y f(v)...
Problem 5. (20 pts) Let f(y) be the real function f: R R depicted in Figurei,...
Problem 5. (20 pts) Let f(y) be the real function f: R R depicted in Figurei, and consider the autonomous differential equation y(t) = f(y(t)). fly) у FIGURE 1. The function f(y) for Problem 4. (a) How many constant solutions does the above differential equation have ? (b) Study whether the behaviour of each of the constant solutions of the differential equation y(t) = f(y(t)) is stable, unstable or semistable. (c) Discuss the long-term behaviour of all solutions y(t) to...
Say you have an autonomous differential equation x' = f(x) and you have found a critical...
Say you have an autonomous differential equation x' = f(x) and you have found a critical point x*. Assuming you don't want to make a plot, what quantity can you examine to possibly find out whether x* is a stable or an unstable equilibrium? Select one: o a. del O b. f (x*) O CZU O d. x*(t)
(1 point) Suppose y = 7x In r. Find the differential: dy = dr. We were...
(1 point) Suppose y = 7x In r. Find the differential: dy = dr. We were unable to transcribe this image(1 point) Consider the function f(x) = –2r3 +33x2 – 144x + 2. (a) Find all critical numbers c off. C= (b) f is increasing for re (c) f is decreasing for se Note: Input U, infinity, and -infinity for union, o, and -o, respectively. If there are multiple answers, separate them by commas. If there is no answer, input...
(1 point) Determine the two singular points of the differential equation (x2-49)y" + (7-x)y' + (r...
(1 point) Determine the two singular points of the differential equation (x2-49)y" + (7-x)y' + (r' + 14x + 49)y-0 List the points in increasing order: Xi = X2 Which of the following statements correctly describes the behaviour of the solutions of the differential equation near the singular point x A. All solutions remain bounded near xi. B. All non-zero solutions are unbounded near C. At least one non-zero solution remains bounded near x and at least one solution is...
3. DO NOT USE CALCULATOR for this problem! Find the EXACT VALUES for all the parts. Given the function f(x,y) (a) Calculate the total differential of z at the point (x, y, z) (b) Use the total dif...
3. DO NOT USE CALCULATOR for this problem! Find the EXACT VALUES for all the parts. Given the function f(x,y) (a) Calculate the total differential of z at the point (x, y, z) (b) Use the total differential to estimate the value of f(1+2(10200),-1 3(10-200). [ Hint : dz= 2(10-200) dy=_3(10-200)]. (c) Calculate the exact diffe ( f(1.-) I Note: total differentiala exact difference. ] rence of f(1+2(10-200)10 200))- (d) Find an equation for the plane s-L(x,y) tangent t(:-: f(z,y)...
1) Write a differential equation describing this system. This means find the equation of the line in the graph. df ar= 1x-80 2) Find the general solution to this differential equation. Find the funct...
1) Write a differential equation describing this system. This means find the equation of the line in the graph. df ar= 1x-80 2) Find the general solution to this differential equation. Find the function f(x) whose derivative is the equation of the line graphed. The solution is: f(r) -.5x 2-80x 3) Now given that function f(x) includes the point (0, 100) find the exact solution of the differential equation found in 1). In addition to general solution you will have...
Problem 1. (1 point) A function y(t) satisfies the differential equation ay = – 44 –...
Problem 1. (1 point) A function y(t) satisfies the differential equation ay = – 44 – 6y2 + 7y?. (a) What are the constant solutions of this equation? Separate your answers by commas. (b) For what values of y is y increasing? <y< Note: You can earn partial credit on this problem.
need help with these, plus checking if valid? please show work! 28) The differential equation with the given direct...
need help with these, plus checking if valid? please show
work!
28) The differential equation with the given direction field has 0.5 and 1.5 as equilibria A) 0.5 is unstable and 1.5 is locally stable B)1.5 is unstable and 0.5 is locally stable C) both are unstable D) both are locally stable R 29) Find the volume of the solid generated by revolving the region bounded by y 2x+3 and y=0, between x 0 and x ANT 1 about the...
4 Consider the autonomous differential equation y f(v) a) (3 points) Find all the equilibrium solutions (critical points). b) (3 points) Use the sign of y f(z) to determine where solutions are increasing / decreasing. Sketch several solution curves in each region determined by the critical points in c) (3 points) the ty-plane. d) (3 points) Classify each equilibrium point as asymptotically stable, unstable, or semi-stable and draw the corresponding phase line.
4 Consider the autonomous differential equation y f(v)...
Problem 5. (20 pts) Let f(y) be the real function f: R R depicted in Figurei, and consider the autonomous differential equation y(t) = f(y(t)). fly) у FIGURE 1. The function f(y) for Problem 4. (a) How many constant solutions does the above differential equation have ? (b) Study whether the behaviour of each of the constant solutions of the differential equation y(t) = f(y(t)) is stable, unstable or semistable. (c) Discuss the long-term behaviour of all solutions y(t) to...
Say you have an autonomous differential equation x' = f(x) and you have found a critical point x*. Assuming you don't want to make a plot, what quantity can you examine to possibly find out whether x* is a stable or an unstable equilibrium? Select one: o a. del O b. f (x*) O CZU O d. x*(t)
(1 point) Suppose y = 7x In r. Find the differential: dy = dr. We were unable to transcribe this image(1 point) Consider the function f(x) = –2r3 +33x2 – 144x + 2. (a) Find all critical numbers c off. C= (b) f is increasing for re (c) f is decreasing for se Note: Input U, infinity, and -infinity for union, o, and -o, respectively. If there are multiple answers, separate them by commas. If there is no answer, input...
(1 point) Determine the two singular points of the differential equation (x2-49)y" + (7-x)y' + (r' + 14x + 49)y-0 List the points in increasing order: Xi = X2 Which of the following statements correctly describes the behaviour of the solutions of the differential equation near the singular point x A. All solutions remain bounded near xi. B. All non-zero solutions are unbounded near C. At least one non-zero solution remains bounded near x and at least one solution is...
3. DO NOT USE CALCULATOR for this problem! Find the EXACT VALUES for all the parts. Given the function f(x,y) (a) Calculate the total differential of z at the point (x, y, z) (b) Use the total differential to estimate the value of f(1+2(10200),-1 3(10-200). [ Hint : dz= 2(10-200) dy=_3(10-200)]. (c) Calculate the exact diffe ( f(1.-) I Note: total differentiala exact difference. ] rence of f(1+2(10-200)10 200))- (d) Find an equation for the plane s-L(x,y) tangent t(:-: f(z,y)...
1) Write a differential equation describing this system. This means find the equation of the line in the graph. df ar= 1x-80 2) Find the general solution to this differential equation. Find the function f(x) whose derivative is the equation of the line graphed. The solution is: f(r) -.5x 2-80x 3) Now given that function f(x) includes the point (0, 100) find the exact solution of the differential equation found in 1). In addition to general solution you will have...
Problem 1. (1 point) A function y(t) satisfies the differential equation ay = – 44 – 6y2 + 7y?. (a) What are the constant solutions of this equation? Separate your answers by commas. (b) For what values of y is y increasing? <y< Note: You can earn partial credit on this problem.
need help with these, plus checking if valid? please show
work!
28) The differential equation with the given direction field has 0.5 and 1.5 as equilibria A) 0.5 is unstable and 1.5 is locally stable B)1.5 is unstable and 0.5 is locally stable C) both are unstable D) both are locally stable R 29) Find the volume of the solid generated by revolving the region bounded by y 2x+3 and y=0, between x 0 and x ANT 1 about the...
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