Homework Answers
Consider the initial value problem y'' – 2y' – 8y = 0, y(0) = a, y'(0)...
Consider the initial value problem y'' – 2y' – 8y = 0, y(0) = a, y'(0) = 6 Find the value of a so that the solution to the initial value problem approaches zero as t + oo Q = a =
Consider the initial value problem y'' + 2y' – 15y = 0, y0) = a, y'0...
Consider the initial value problem y'' + 2y' – 15y = 0, y0) = a, y'0 = 1 Find the value of a so that the solution to the initial value problem approaches zero as t → a= Preview Get help: Video Points possible: 2 Unlimited attempts.
Solve 2y'' – 5y' – 25y = 0, y(0) = -6, y'(0) = – 15 (t)...
Solve 2y'' – 5y' – 25y = 0, y(0) = -6, y'(0) = – 15 (t) = Consider the initial value problem y' + 3y' – 10y = 0, y(0) = a, y'(0) = 3 Find the value of a so that the solution to the initial value problem approaches zero as t + oo a = 1
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...
Solve the initial value problem y" – 2y' + 5y = 0; y(0) = 2, y'(0)...
Solve the initial value problem y" – 2y' + 5y = 0; y(0) = 2, y'(0) = -4. For answer from (a), determine lim y(t).
Consider the initial value problem y'' + y' – 12y = 0, y(0) = a, y'(0)...
Consider the initial value problem y'' + y' – 12y = 0, y(0) = a, y'(0) = 5 Find the value of a so that the solution to the initial value problem approaches zero ast → a = Preview
Let Lyl = y + 2y + y (a) Solve the initial value problem L[y]=0 y(0)=1...
Let Lyl = y + 2y + y (a) Solve the initial value problem L[y]=0 y(0)=1 (y'0)=1 (b) Use the method of undetermined coefficients to find a particular solution to the equation L[y] =2e-4
1. (5 points) Use a Laplace transform to solve the initial value problem: y' + 2y...
1. (5 points) Use a Laplace transform to solve the initial value problem: y' + 2y + y = 21 +3, y(0) = 1,5 (0) = 0. 2. (5 points) Use a Laplace transform to solve the initial value problem: y + y = f(t), y(0) = 1, here f(0) = 2 sin(t) if 0 Str and f(0) = 0 otherwise.
Solve the initial value problem y" + 3y' + 2y = 8(t – 3), y(0) =...
Solve the initial value problem y" + 3y' + 2y = 8(t – 3), y(0) = 2, y'(0) = -2. Answer: y = u3(t) e-(-3) - u3(t)e-2(1-3) + 2e-, y(t) ={ 2e-, t<3, -e-24+6 +2e-l, t>3. 5. [18pt] b) Solve the initial value problem y' (t) = cost + Laplace transforms. +5° 867). cos (t – 7)ds, y(0) – 1 by means of Answer:
Using Laplace transforms, solve the initial value problem y' = 2y + 3e-t, y(0) = 4,...
Using Laplace transforms, solve the initial value problem y' = 2y + 3e-t, y(0) = 4, where y' = Note: to check your work, this equation is linear so it is possible to solve using integrating factors also. 17 Marks) Y
Consider the initial value problem y'' – 2y' – 8y = 0, y(0) = a, y'(0) = 6 Find the value of a so that the solution to the initial value problem approaches zero as t + oo Q = a =
Consider the initial value problem y'' + 2y' – 15y = 0, y0) = a, y'0 = 1 Find the value of a so that the solution to the initial value problem approaches zero as t → a= Preview Get help: Video Points possible: 2 Unlimited attempts.
Solve 2y'' – 5y' – 25y = 0, y(0) = -6, y'(0) = – 15 (t) = Consider the initial value problem y' + 3y' – 10y = 0, y(0) = a, y'(0) = 3 Find the value of a so that the solution to the initial value problem approaches zero as t + oo a = 1
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...
Solve the initial value problem y" – 2y' + 5y = 0; y(0) = 2, y'(0) = -4. For answer from (a), determine lim y(t).
Consider the initial value problem y'' + y' – 12y = 0, y(0) = a, y'(0) = 5 Find the value of a so that the solution to the initial value problem approaches zero ast → a = Preview
Let Lyl = y + 2y + y (a) Solve the initial value problem L[y]=0 y(0)=1 (y'0)=1 (b) Use the method of undetermined coefficients to find a particular solution to the equation L[y] =2e-4
1. (5 points) Use a Laplace transform to solve the initial value problem: y' + 2y + y = 21 +3, y(0) = 1,5 (0) = 0. 2. (5 points) Use a Laplace transform to solve the initial value problem: y + y = f(t), y(0) = 1, here f(0) = 2 sin(t) if 0 Str and f(0) = 0 otherwise.
Solve the initial value problem y" + 3y' + 2y = 8(t – 3), y(0) = 2, y'(0) = -2. Answer: y = u3(t) e-(-3) - u3(t)e-2(1-3) + 2e-, y(t) ={ 2e-, t<3, -e-24+6 +2e-l, t>3. 5. [18pt] b) Solve the initial value problem y' (t) = cost + Laplace transforms. +5° 867). cos (t – 7)ds, y(0) – 1 by means of Answer:
Using Laplace transforms, solve the initial value problem y' = 2y + 3e-t, y(0) = 4, where y' = Note: to check your work, this equation is linear so it is possible to solve using integrating factors also. 17 Marks) Y
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