#6 Solve the initial value problem y(0)- 2, y,(0) 1 y"-3y' + 2y-6(t-3);
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:
Problem 1: Solve the initial value problems: a 2y" – 3y' +y=0 y(0) = 2, 7(0) = 1 by' + y - 6y = 0 y(0) = -1, y'(0) = 2 cy' + 4y + 3y = 0 y(0) = 1, y'(0) = 0 Problem 2: Solve the initial value problems: a y' +9y = 0 y(0) = 1. 1'(0) = -1 by" - 4y + 13y = 0 y(0) = 1, y'(0) = 3 cy" + ly + ly...
2. Use the Laplace Transform to solve the initial value problem y"-3y'+2y=h(t), y(O)=0, y'(0)=0, where h (t) = { 0,0<t<4 2, t>4
Consider the initial value problem y" +3y' +2y = (t-1)+r(t), y(0) = y(0) = 0, where 8(t-1) is Dirac's delta function and S4 if 0<t<1 r(t) 8 if t > 1 (a) Represent r(t) using unit step functions. (b) Find the Laplace Transform of 8(t-1)+r(t). (c) Solve the above initial value problem. {
5. (11 points) Solve the following initial value problem, y" + 3y + 2y = g(t); y(0) = 0, 7(0) = 1/2 where g(t) = 38(t - 1) + uz(t) Type here to search
Solve the initial value problem y" – 3y' + 2y = e3r, y(0) = 2, y'(0) = -1. (a) y(x) = 40-1 – 4e2+ 2e 32 (b) y(x) = 1 e?' – 4e-2x + £230 (c) y(x) = 40-1 – 4e-2x + 3e3x (d) y(x) = 40" – 4e2x + e3r Select one: a с b d
Solve the initial value problem below using the method of Laplace transforms. y" + 2y-3y® 0, y(0)-2, y'(0)-6
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
Use the Laplace transform to solve the initial value problem: y" - 3y' + 2y = 4t + ezt, y(0) = 1, y'(0) = -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...