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Problem 6: Verify that the problem y' -y13 and y(0) 0 Has two solutions: y-0 and y = (m3/2 which of the solutions would be reproduced by numerical integration if the initial condition is set at (...
4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the...
4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the integrating factor method. (b) What is the largest interval on which its solution is guaranteed to uniquely exist? (c) The equation is also separable. Solve it again as a separable equation. Find the particular solution of this IVP. Does your answer agree with that of part (a)? 5 Find the general solution of the differential equation. Do not solve explicitly for y. 6,/Solve explicitly...
2. -13 points ZillDiffEQModAp111.1.011. 0/6 Submissions Used My Notes Verify that the indicated function is an...
2. -13 points ZillDiffEQModAp111.1.011. 0/6 Submissions Used My Notes Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate intervall of definition for the solution. 6y + y = 0; y = e-x/6 When y = e-x/6 y'a Thus, in terms of x, 6y' + y = 3. -12 points ZillDiffEQModAp111.2.001. 0/6 Submissions Used My Notes Ask Your Teacher In this problem, y = 1/(1+ce) is a one-parameter family of solutions of the...
Problem 2. (a) Solve the initial value problem I y' + 2y = g(t), 1 y(0)...
Problem 2. (a) Solve the initial value problem I y' + 2y = g(t), 1 y(0) = 0, where where | 1 if t < 1, g(t) = { 10 if t > 1 (t) = { for all t. Is this solution unique for all time? Is it unique for any time? Does this contradict the existence and uniqueness theorem? Explain. (b) If the initial condition y(0) = 0 were replaced with y(1) = 0, would there necessarily be...
Complete using MatLab 1. Consider the following initial value problem 3t2-y, y(0) = 1 Using Euler's...
Complete using MatLab
1. Consider the following initial value problem 3t2-y, y(0) = 1 Using Euler's Method and the second order Runge-Kutta method, for t E [0, 1] with a step size of h 0.05, approximate the solution to the initial value problem. Plot the true solution and the approximate solutions on the same figure. Be sure to label your axis and include an a. appropriate legend b. Verify that the analytic solution to the differential equation is given by...
Find the solution of the following initial value problem. y'' (t) = 6te! y(0) = 3,...
Find the solution of the following initial value problem. y'' (t) = 6te! y(0) = 3, y'(0) = 1 y(t) = Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when Ris revolved about the x-axis. y = 21 - x, y=x, and y = 0 Set up the integral that gives the volume of the solid. Use increasing limits of integration. Select the correct choice below...
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0,...
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
(a) You are given that two solutions of the homogeneous Euler-Cauchy equation, da2 are y,-z-6 and y2 2 Confirm the linear independence of your two solutions (for z >0) by computing their Wron...
(a) You are given that two solutions of the homogeneous Euler-Cauchy equation, da2 are y,-z-6 and y2 2 Confirm the linear independence of your two solutions (for z >0) by computing their Wronskian, (b) Use variation of parameters to find a particular solution of the inhomogeneous Euler-Cauchy equation, d r (O) First, enter your expression foru(as defined in lectures) below da 上一题 退出并保存 提交试卷 (b) Use variation of parameters to find a particular solution of the inhomogeneous Euler-Cauchy equation, d...
Problem 1. Consider the following initial value problem: d = 3t+y+1, (0) - 4. Denote the...
Problem 1. Consider the following initial value problem: d = 3t+y+1, (0) - 4. Denote the solution of the initial value problem by 9 (a) Use the method for solving linear differential equations from Chapter 1 (using an integrating factor) to find the exact solution to the initial value problem. (b) Use the Improved Euler's method to estimate 9(0.2) using a step size of At -0.1 in other words, using two steps). Answer this by filling out a table like...
Exercise 2 (20 marks). Let a be a real number and consider the following numerical method...
Exercise 2 (20 marks). Let a be a real number and consider the following numerical method to approximate the solutions to the IVP y' = f(y) with initial condition y(0) = yo: starting from yo, for all n > 0 define yn+1 by Yn+1 = yn + f(y) (first predictor) ent1 = yn + ** f (yn) (second predictor) Yn+1 = yn + h [af (y*+1) + (1 - a)f (y*+1)] (corrector). 1. (5 marks) The quantities yn+1 and y**1...
5. Find the solution of the heat conduction problem for each initial condition given: Suxxx =...
5. Find the solution of the heat conduction problem for each initial condition given: Suxxx = 0<x<211, tu(0,1) = 0, tu(27,1) = 0, t> 0. (a) u(x,0) =(x) = -2sin(3x) - 3sin(4x) + 17sin(9x/2). (b) u(x,0) = f(x) = 8. (Hint: You may skip the integrations by using the result of #2(b).] (c) In each of cases (a) and (b), find the limit of u( 71,1) ast approaches 0. Are they different? Did you expect them to be different? 6....
4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the integrating factor method. (b) What is the largest interval on which its solution is guaranteed to uniquely exist? (c) The equation is also separable. Solve it again as a separable equation. Find the particular solution of this IVP. Does your answer agree with that of part (a)? 5 Find the general solution of the differential equation. Do not solve explicitly for y. 6,/Solve explicitly...
2. -13 points ZillDiffEQModAp111.1.011. 0/6 Submissions Used My Notes Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate intervall of definition for the solution. 6y + y = 0; y = e-x/6 When y = e-x/6 y'a Thus, in terms of x, 6y' + y = 3. -12 points ZillDiffEQModAp111.2.001. 0/6 Submissions Used My Notes Ask Your Teacher In this problem, y = 1/(1+ce) is a one-parameter family of solutions of the...
Problem 2. (a) Solve the initial value problem I y' + 2y = g(t), 1 y(0) = 0, where where | 1 if t < 1, g(t) = { 10 if t > 1 (t) = { for all t. Is this solution unique for all time? Is it unique for any time? Does this contradict the existence and uniqueness theorem? Explain. (b) If the initial condition y(0) = 0 were replaced with y(1) = 0, would there necessarily be...
Complete using MatLab
1. Consider the following initial value problem 3t2-y, y(0) = 1 Using Euler's Method and the second order Runge-Kutta method, for t E [0, 1] with a step size of h 0.05, approximate the solution to the initial value problem. Plot the true solution and the approximate solutions on the same figure. Be sure to label your axis and include an a. appropriate legend b. Verify that the analytic solution to the differential equation is given by...
Find the solution of the following initial value problem. y'' (t) = 6te! y(0) = 3, y'(0) = 1 y(t) = Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when Ris revolved about the x-axis. y = 21 - x, y=x, and y = 0 Set up the integral that gives the volume of the solid. Use increasing limits of integration. Select the correct choice below...
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
(a) You are given that two solutions of the homogeneous Euler-Cauchy equation, da2 are y,-z-6 and y2 2 Confirm the linear independence of your two solutions (for z >0) by computing their Wronskian, (b) Use variation of parameters to find a particular solution of the inhomogeneous Euler-Cauchy equation, d r (O) First, enter your expression foru(as defined in lectures) below da 上一题 退出并保存 提交试卷 (b) Use variation of parameters to find a particular solution of the inhomogeneous Euler-Cauchy equation, d...
Problem 1. Consider the following initial value problem: d = 3t+y+1, (0) - 4. Denote the solution of the initial value problem by 9 (a) Use the method for solving linear differential equations from Chapter 1 (using an integrating factor) to find the exact solution to the initial value problem. (b) Use the Improved Euler's method to estimate 9(0.2) using a step size of At -0.1 in other words, using two steps). Answer this by filling out a table like...
Exercise 2 (20 marks). Let a be a real number and consider the following numerical method to approximate the solutions to the IVP y' = f(y) with initial condition y(0) = yo: starting from yo, for all n > 0 define yn+1 by Yn+1 = yn + f(y) (first predictor) ent1 = yn + ** f (yn) (second predictor) Yn+1 = yn + h [af (y*+1) + (1 - a)f (y*+1)] (corrector). 1. (5 marks) The quantities yn+1 and y**1...
5. Find the solution of the heat conduction problem for each initial condition given: Suxxx = 0<x<211, tu(0,1) = 0, tu(27,1) = 0, t> 0. (a) u(x,0) =(x) = -2sin(3x) - 3sin(4x) + 17sin(9x/2). (b) u(x,0) = f(x) = 8. (Hint: You may skip the integrations by using the result of #2(b).] (c) In each of cases (a) and (b), find the limit of u( 71,1) ast approaches 0. Are they different? Did you expect them to be different? 6....
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