Solve y'' + 4y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 fort > 6
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
differential equations Problem 2 Solve y"+y= ſt/2, if 0 <t<6, if t > 6 y(0) = 6, 7(0) = 8
Solve the following initial value problem. St/2 if 0 <t<6 y" +y= 3 ift > 6 6 y(0) = y'(0) = 0 14Pm1011* 1917 Prid A++ V "Top14
(1 point) Consider the following initial value problem: 4t, 0<t<8 \0, y" 9y y(0)= 0, y/(0) 0 t> 8 Using Y for the Laplace transform of y(t), i.e., Y = L{y(t)} find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)
+ 2y = 4u, y(0) = 0, for the following input: Solve: dt 0<t<T u(t) t>T Graph the solution (you may use Excel or Matlab) for T= 1sec, 0.1sec, 0.01sec, and 0.001sec. Do you see what is happening to the output? What is happening to the input?!
2y + y + 2y = g(t), (O) = 0, y'(0) = 0 where g) 5 St<20 10, 0<t<5 and t > 20
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
(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)
So 0<t<5 Using the Laplace transform, solve the initial value problem y' + y = 3 t5 y'(0) = 0. 9