Laplace transform 0 <t<1 3. y' -5y = 10 t21 y(0)=1
Laplace transform of the unit step function y" + 4y = ſi, if 0 <t<, y(0) = 0, y'(0) = 0. 10, if a St<oo.'
2. Given 12 f(t)= ={ Ost<3 t23 (a) Write f(t) in one line using the unit step function (Heaviside function). 5 points 10 points (b) Find L{f(t)}, either by using the definition of the Laplace transform or by finding the Laplace transform of your answer to part (a).
Find the Laplace transform of the given function Solve the integral equation f(t) = { 0 < t < 2 t 22 t y(t) = 4t – 3 y(z)sin(t – z)dz 0
The Laplace transform of the plecewise continuous function f(t) = S4, 0<t<3 12, t> 3 Is given by [{f} = { (3 – e-"), o>0. None of them 1 [{f} = (1 – 2e-4), 8>0. 0 [11] = (1 – 3e-4), 0> 0. ° L{f} = { (2–e=4), o>0.
(1 point) Consider the initial value problem y' + 3y = 0 if 0 <t <3 9 if 3 < t < 5 0 if 5 <t< oo, y(0) = 3. (a) Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y by Y. Do not move any terms from one side of the equation to the other (until you get to part (b) below). y(s)(5+6)...
Find the Laplace Transform of f(t)=0 if t<1: f(t) = t if 13t<2; f(t) = 0 ift> 2.
t?, t<3 . Express the function f(t) = le4t, 3St<5 In terms of unit step functions and compute it's Laplace transform
QUESTION 7 Find the Laplace transform of the function f(t) = t, 0 <t<1 1, t>1 S e S s2 - e-s S 1 e-(s-1) S 32 S e OD. 1- $2 - e $2
QUESTION 1 5 Find the Laplace transform of the function f(t) t, 0<t<1 1, t > 1