(a) For the solution that satisfies y(0) = 0, sketch the solution curve and estimate the following
Consider the slope field shown.
(a) For the solution that satisfies y(0) = 0, sketch the solution curve and estimate the following
(b) For the solution that satisfies y(0) = 1, sketch the solution curve and estimate the following:
(c) For the solution that satisfies y(0) = -1, sketch the solution curve and estimate the following
Homework Answers
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(a) For the solution that satisfies y(0) = 0, sketch the solution curve and estimate the following
Section 1.1 Direction Fields: Problem 9 Previous Problem Problem List Next Problem (1 point) Cons...
Section 1.1 Direction Fields: Problem 9 Previous Problem Problem List Next Problem (1 point) Consider the slope field shown (a) For the solution that satisfies y(0) -0, sketch theEBM solution curve and estimate the following: y(1) A and y(-1) (b) For the solution that satisfies y(0) 1, sketch the solution curve and estimate the following: y(0.5) A t and y(-1) (c) For the solution that satisfies y(0) =-1 , sketch the solution curve and estimate the following: and y(-1)
Section...
(a) Solve the following initial value problem: dy/dx = (y^2 − 4) / x^2 y(1) =...
(a) Solve the following initial value problem: dy/dx = (y^2 − 4) / x^2 y(1) = 0 (b) Sketch the slope field in the square −4 <x< 4,−4 <y< 4, and draw several solution curves. Mark the solution curve corresponding to your solution. (c) What is the long term behaviour of the solution from (a) as x → +∞? Is it defined for all x? (d) Find the only solution that satisfies lim(x→+∞) y(x) = 2, and explain why there...
Problem 6. Consider the system: y. and its corresponding vector field: 1. Sketch a number of diff...
Problem 6. Consider the system: y. and its corresponding vector field: 1. Sketch a number of different solution curves on the phase plane. 2. Describe the behavior of the solution that satisfies the initial condition (to, o) (0, 2)
Problem 6. Consider the system: y. and its corresponding vector field: 1. Sketch a number of different solution curves on the phase plane. 2. Describe the behavior of the solution that satisfies the initial condition (to, o) (0, 2)
Reproduce the given computer-generated direction field. Then sketch an approximate solution curve that passes through each...
Reproduce the given computer-generated direction field. Then sketch an approximate solution curve that passes through each of the indicated points. dy-- dx (a) y(-2) = 1 (ь) у(3) - 0 (c) y(0) 2 (d) y(0) 0
Reproduce the given computer-generated direction field. Then sketch an approximate solution curve that passes through each of the indicated points. dy-- dx
(a) y(-2) = 1
(ь) у(3) - 0
(c) y(0) 2
(d) y(0) 0
Euler's Method reliminary Example. In the figure below, you are given the slope field for an initial value problen of the dy = F(z, v), y(0) = 0. Derive a tmethod for approximating the soluti...
Euler's Method reliminary Example. In the figure below, you are given the slope field for an initial value problen of the dy = F(z, v), y(0) = 0. Derive a tmethod for approximating the solution curve v(x) for this initial value problenm. 3.5 Euler's Method Formulas: Examples and Exercises 1. Consider the initial value problem 1.5 dr a To the right, you are given a slope field and a 0.8 ////////////w/./10.8 graph of the unknown solution to this problem, (x)....
Sketch the slope field of y' = ty to determine lim --- y(t) such that y...
Sketch the slope field of y' = ty to determine lim --- y(t) such that y is a solution with y(0) < 0. The limit is 00 -00 -1
Consider the following slope field. SF3 4 2 0 -2 1 -4 -10 -5 0 5...
Consider the following slope field. SF3 4 2 0 -2 1 -4 -10 -5 0 5 10 a If a solution curve y passes through the point (-5,2), estimate the value of the function when r = -4, and explain your answer. If a solution curve y passes through the point (-5,2), estimate the value of the function when r = 5, and explain your answer.
17. Consider the differential equation given by dy/dx = xy/2
17. Consider the differential equation given by dy/dx = xy/2 (A) On the axes provided, sketch a slope field for the given differential equation. (B) Let f be the function that satisfies the given differential equation. Write an equation for the tangent line to the curve y (x) through the point (1, 1). Then use your tangent line equation to estimate the value of f(1.2) (C) Find the particular solution y=f(x) to the differential equation with the initial condition f(1)=1. Use your solution...
Consider the following logistic equation for t2 0. Sketch the direction field, draw the solution curve...
Consider the following logistic equation for t2 0. Sketch the direction field, draw the solution curve for each initial condition, and find the equilibrium solutions. Assume t20 and P0. P P' (t) = 0.02P 1- 300 P(O) = 100, P(O) = 200, P(O) = 400 OA P 1000 OB P 1000 O c. P 1000 OD P 1000 750 750 750 750 500 500 500 500 250 2501 250 250 100 200 300 400 100 200 300 400 100 200...
The slope field for the equation dy/dx = x+y for −4 ≤ x ≤ 4, −4 ≤ y ≤ 4 is shown in the figure be...
The slope field for the
equation dy/dx = x+y for −4 ≤ x ≤ 4, −4 ≤ y ≤ 4
is shown in the figure below.
The slope field for the equation yxy for -4 SxS4, -4 Sy s4 is shown in the figure below TA (a) Sketch the solutions that pass through the following points: -Select The solution has slope at (0, 0) and is Concave up concave down inear (ü) (-3, 1)increasing The solution sdecreasing -Select concave up...
Section 1.1 Direction Fields: Problem 9 Previous Problem Problem List Next Problem (1 point) Consider the slope field shown (a) For the solution that satisfies y(0) -0, sketch theEBM solution curve and estimate the following: y(1) A and y(-1) (b) For the solution that satisfies y(0) 1, sketch the solution curve and estimate the following: y(0.5) A t and y(-1) (c) For the solution that satisfies y(0) =-1 , sketch the solution curve and estimate the following: and y(-1)
Section...
Problem 6. Consider the system: y. and its corresponding vector field: 1. Sketch a number of different solution curves on the phase plane. 2. Describe the behavior of the solution that satisfies the initial condition (to, o) (0, 2)
Problem 6. Consider the system: y. and its corresponding vector field: 1. Sketch a number of different solution curves on the phase plane. 2. Describe the behavior of the solution that satisfies the initial condition (to, o) (0, 2)
Reproduce the given computer-generated direction field. Then sketch an approximate solution curve that passes through each of the indicated points. dy-- dx (a) y(-2) = 1 (ь) у(3) - 0 (c) y(0) 2 (d) y(0) 0
Reproduce the given computer-generated direction field. Then sketch an approximate solution curve that passes through each of the indicated points. dy-- dx
(a) y(-2) = 1
(ь) у(3) - 0
(c) y(0) 2
(d) y(0) 0
Euler's Method reliminary Example. In the figure below, you are given the slope field for an initial value problen of the dy = F(z, v), y(0) = 0. Derive a tmethod for approximating the solution curve v(x) for this initial value problenm. 3.5 Euler's Method Formulas: Examples and Exercises 1. Consider the initial value problem 1.5 dr a To the right, you are given a slope field and a 0.8 ////////////w/./10.8 graph of the unknown solution to this problem, (x)....
Sketch the slope field of y' = ty to determine lim --- y(t) such that y is a solution with y(0) < 0. The limit is 00 -00 -1
Consider the following slope field. SF3 4 2 0 -2 1 -4 -10 -5 0 5 10 a If a solution curve y passes through the point (-5,2), estimate the value of the function when r = -4, and explain your answer. If a solution curve y passes through the point (-5,2), estimate the value of the function when r = 5, and explain your answer.
Consider the following logistic equation for t2 0. Sketch the direction field, draw the solution curve for each initial condition, and find the equilibrium solutions. Assume t20 and P0. P P' (t) = 0.02P 1- 300 P(O) = 100, P(O) = 200, P(O) = 400 OA P 1000 OB P 1000 O c. P 1000 OD P 1000 750 750 750 750 500 500 500 500 250 2501 250 250 100 200 300 400 100 200 300 400 100 200...
The slope field for the
equation dy/dx = x+y for −4 ≤ x ≤ 4, −4 ≤ y ≤ 4
is shown in the figure below.
The slope field for the equation yxy for -4 SxS4, -4 Sy s4 is shown in the figure below TA (a) Sketch the solutions that pass through the following points: -Select The solution has slope at (0, 0) and is Concave up concave down inear (ü) (-3, 1)increasing The solution sdecreasing -Select concave up...
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