2. (a) Find Laplace transform of tecosht s2 - 65+7 (b) Find inverse Laplace transform of (52 – 4s +5)
Q3. Find the inverse Laplace transform of the following: a) 1 2 s+5)(s +4s +5)
Find the inverse Laplace transform of the following expression. 8s + 4 52 - 4s + 40
Problem 5. Determine the inverse Laplace transform of Problem 6. Determine the inverse Laplace transform of 2s2 4s 10 9(s) = 2(s+1) Problem 7. Determine the inverse Laplace transform of 2s 10
1. (10 points) Find the inverse Laplace transform of the following: 85 - 4s +12 s? +45-5 b. F(x) = s(s? +2s + 5) 2. (10 points) Determine if the following differential equation is exact. Be sure give a reason for why or why not. If it is exact, solve it. (xy? + 3x y)+(x° +xºy)y'=0 a. F(s)= (1-25)e-
e +e- 4. a. Find the inverse Laplace transform of b. Find the inverse Laplace transform f(t) of: then sketch the graph of f(t).
Q3 Find the inverse Laplace transform for the following expression [20] i. F(s) 10 4s +11 s2+118+10 65° +105+2 $3+352 +2s ii. F(S) 10
Determine the inverse Laplace transform of the function below. -5s Se $2 + 4s + 13 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. -5s se (t) +48 + 13 (Use parentheses to clearly denote the argument of each function.) s2+
Find the inverse Laplace transform a . 3 s4 - 2s s2 (3s2 + 4) 3 S4 – 25 (s + 1)(3s2 + 4s + 2) b.
6. (a) Determine the inverse Laplace transform of F(8) 2s - 1 32 - 4s +6 (10 marks/ (b) Solve the initial value problem using the method of Laplace transform. 7+10y = 0, y(0) = 0, (0) --3. (20 marks) (c) Solve the initial value problem: 1 dy dy 4 dx2 + 4y = 0, y(0) -- da + (0) = -1 120 marks)