Problem 3: Solve the initial value problem and write your solution as a piecewise func- tion:...

Question

Question

Problem 3: Solve the initial value problem and write your solution as a piecewise func- tion: y () y(0) A,y(0) with cos(2t),

Answer 1

Answer #1

cos 2t+cos(2t -12 if t>6 cos 2t if t 6 f(t)- cos 2t+cos (2t-12)u(t-6) ()-cos 2t+cos(2(e-6(t-6) S +4 y-y낙(1) s +4 -4s +4 y(s)

Answer 2

Similar Homework Help Questions

do 2 and 3 Example 2.4. Find a solution to the initial value problem tion of...

do 2 and 3 Example 2.4. Find a solution to the initial value problem tion of variables. = xy'), y(0) = 0 by separa- = 220/2 dx dy =xda yv f yolkdy - freda 1/2 y 2 Vy = 22 + c y colo 200) = 0 + c cao = 25 = 22 - ² - 4 Vy Show that the theorem on eristence and uniqueness of first-order initial value problems (See See ) does not guarantee that this...
3. Use Laplace transforms to solve the following initial value problems. Write the solution (t) f...

3. Use Laplace transforms to solve the following initial value problems. Write the solution (t) for t20 as a simplified piecewise defined function. (a) z', + 2x' + 2x-f(t), x(0-0, z'(0)-i, where f(t)-〈0 otherwise. (b) z', +x-f(t), x(0) 0, z'(0)=1, where t/2 if 0 t< 6, 3 ift26 f(t) 3. Use Laplace transforms to solve the following initial value problems. Write the solution (t) for t20 as a simplified piecewise defined function. (a) z', + 2x' + 2x-f(t), x(0-0, z'(0)-i,...
Differential Equations (1) (a)]Define solution to a a differential equation. Given an example of func- tion...

Differential Equations (1) (a)]Define solution to a a differential equation. Given an example of func- tion that is a solution and example of a function that is not a solution to a given differential equation. (b) Solve the initial value problem y' = 4y2 +ry², y(0) = 1.

use the Laplace transform to solve the given initial value problem: Only problem 4,8 and 12...

use the Laplace transform to solve the given initial value problem: Only problem 4,8 and 12 please 4. y" – 4y' + 4y = 0; y(0) = 1, y'(0) = 1 5. y" – 2y' + 4y = 0; y(0) = 2, y'(0) = 0 Σ Answer Solution = e 6. y" + 4y' + 297 - 2t sin 5t; y(0) = 5, 7. y" +12y = cos 2t, 22 # 4; y(0) = 1, : > Answer > Solution...
Solve initial value problem using Laplace transform Problem 4 Solve the initial value problems given below...

Solve initial value problem using Laplace transform Problem 4 Solve the initial value problems given below --ез, y(0) 2. a. b. f ty 3 cos t, y(0)-
Question 7 < > Solve the initial-value problem using the Method of Undeterminded Coefficients: y' +...

Question 7 < > Solve the initial-value problem using the Method of Undeterminded Coefficients: y' + 4y = 10 cos(2t) y(0) = 1 y'(0) = 1 g(t) = Submit Question

Find the solution of the initial value problem y" – 2y' + 5y = g(t), y(0)...

Find the solution of the initial value problem y" – 2y' + 5y = g(t), y(0) = 0, y'(0) = 0, where g(t) is a continuous, otherwise arbitrary, function. Oy(t) = g(t) 1 y(t) = (sets sin(2t))g(t) Oy(t) = (cos(2t)) * g(t) Oy(t) = (cos(2t))g(t) y(t) = (1 e*) + f(t) x(t) =() e sin(26)g(t) g(t) = ( e sin(2t) + (t) y(t) = Ce+ sin(2t)) *g(t) 1
Problem 3. Given the initial conditions, y(0) from t- 0 to 4: and y (0 0, solve the following initial-value problem...

Problem 3. Given the initial conditions, y(0) from t- 0 to 4: and y (0 0, solve the following initial-value problem d2 dt Obtain your solution with (a) Euler's method and (b) the fourth-order RK method. In both cases, use a step size of 0.1. Plot both solutions on the same graph along with the exact solution y- cos(3t). Note: show the hand calculations for t-0.1 and 0.2, for remaining work use the MATLAB files provided in the lectures Problem...
1. Solve the initial value problem for a damped mass-spring system acted upon by a sinusoidal...

1. Solve the initial value problem for a damped mass-spring system acted upon by a sinusoidal force for some time interval f(t) = {10 sin 2t 0 0<t< y(0) 1, y'(0) -5 y"2y' 2y f(t), Tt zusor= 2. Consider two masses and three springs without no external force. The resulting force balance can be expressed as two second order ODES shown as below. mx=-(k k2)x1+ kzx2 m2x2 (k2k3)x2 + k2x1 15 If m 2,m2 ki = 1,k2 = 3, k3...

1 point) Consider the initial value problem dy 29y--9e cos( dt dt2 dt Write down the Laplace transform of the left-hand...

1 point) Consider the initial value problem dy 29y--9e cos( dt dt2 dt Write down the Laplace transform of the left-hand side of the equation given the initial conditions Y(sA2-10s+29)+3s-24 Your answer should be a function of s and Y with Y denoting the Laplace transform of the solution y. Write down the Laplace transform of the right-hand side of the equation -9(s-5(S-5)A2+9) Your answer should be a function of s only. Next equate your last two answers and solve...