Solve the following initial value problem. St/2 if 0 <t<6 y" +y= 3 ift > 6...
Solve the y"+ 4y = initial value problem s 1 if 0<xsa To if x>,T ylo)= 1, g(0)=0
differential equations Problem 2 Solve y"+y= ſt/2, if 0 <t<6, if t > 6 y(0) = 6, 7(0) = 8
Solve y'' + 4y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 fort > 6
(1 point) Consider the following initial value problem: y" +9y (st, o<t<8 y(0) = 0, '(0) = 0 132, ?> 8 Using Y for the Laplace transform of y(t), i.e., Y = C{y(t)} find the equation you get by taking the Laplace transform of the differential equation and solve for Y(8)
Solve the initial value problem ry' + xy = 1, > 0 y(1) = 2.
Laplace transform of the unit step function y"+y= St/2, if 0 St<6, 13, if t > 6 y(0) = 6, y'(0) = 8
if t < 41 8(t) = 41 if t > 41 Solve the differential equation y(0) = 6, 7(0) = 5 y" +4y = g(t), using Laplace transforms. ift < 41 if t > 411
Solve y'' +9y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 for t > 6
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...
Apply separation of variables and solve the following boundary value problem 0 < x < t> 0 t>O Ytt(x, t) = 25 yxx(x, t) ya(0,t) = y2(7,t) = y(x,0) = f(x) yt(x,0) = g(x) 0 << 0 <r<a