a=0 find the solution of IVP y" +(a +1)y = e(6+1)t, y(0) = 0,4(0) = 2...
Consider the following IVP y″ + 5y′ + y = f (t), y(0) = 3, y′(0) = 0, where f (t) = { 8 0 ≤ t ≤ 2π cos(7t) t > 2π (a) Find the Laplace transform F(s) = ℒ { f (t)} of f (t). (b) Find the Laplace transform Y(s) = ℒ {y(t)} of the solution y(t) of the above IVP. Consider the following IVP y" + 5y' + y = f(t), y(0) = 3, y'(0) =...
pls do all questions. thanx 1. [5 Consider the IVP rty(t) + 2 sin(t)y(t) = tan(t) y(5)=2 Does a unique solution of the IVP exist? Do not solve the IVP but fully justify you answer. What is the IOE? 2. 4 Consider the ODE Using undetermined coefficients, what is an approprite guess for the coefficient (s) in yp but fully justify you answer. ? Do not solve for 3. [10] Solve the IVP. Use any approach you like y(x) 6y'(x)...
Question 1: [25 pts] Consider the IVP y" – 4y' - 5y = 0, y(0) = 1, y0) = 2. a) Find the solution of the given IVP using the corresponding characteristic equation. b) Find the solution of the IVP using the Laplace Transform. c) Does the solution change if we would change the second initial condition as y'(0)=3? Explain.
Solve the IVP using laplace transformation y”+3y=(t-2)u(t-1) y(0)=-1 y’(0)=2 Solve the IVP usiag laplace transformahbn 3y (t-2) u (t-1) (0) 2 yo)-1 Solve the IVP usiag laplace transformahbn 3y (t-2) u (t-1) (0) 2 yo)-1
Question 2 Given the following second order IVP: y" – 2y' + y = e*, y(0) = 0, y'(0) = 1. 1. Solve it using the undetermined coefficients method. [2 pt] 2. Solve it again using the Laplace Transform. (2.5 pt] 3. Which method did you find easier and why? [0.5 pt]
Find the solution of the given IVP y" + 3y' + 2y = uz(t); y(0) = 0, y'(0) = 1 a. y = et-e-t + uz(t) [] + e-(6+2) +22(6+2) b. y = ef +e-t+uz(t)ſ - e-(6-2) + şe-26-2)] + uz(t) - e-(1-2) 3e=2(-2)] e + C. y = e-t-e-27 d. None of these
Find the laplace transformation for the IVP y''+y=Aδ(t−π/2), y(0)=1, y′(0)=0
Question 1 Given the following first order IVP: -y=e", y(0) = 0 1. Determine if the equation is linear, separable and/or Bernoulli (0.5 pt] 2. Solve the IVP using one of applicable methods studied (integrating factor, separation of variable and/or substitution of variables) (2 pt] 3. Now solve it again using the Laplace Transform [2 pt] 4. Which method did you find easier and why? [0.5 pt]
Question 1 Given the following first order IVP: -y=e", y(0) = 0 1. Determine if the equation is linear, separable and/or Bernoulli (0.5 pt] 2. Solve the IVP using one of applicable methods studied (integrating factor, separation of variable and/or substitution of variables) (2 pt] 3. Now solve it again using the Laplace Transform [2 pt] 4. Which method did you find easier and why? [0.5 pt]
(1 point) Take the Laplace transform of the IVP dy -1 di - y= 0, y(0) = 6 Use Y for the Laplace transform of y, (not Y(s)). II So Y= S- and y(t) =