Question 1: [25 pts] S+1 a) Find the inverse Laplace transform of the expression $2+4 b)...
Find the inverse Laplace transform of the transfer function Q-5 s+1 S+1 25 pts. s3 +2s2+9s+18(s+2)(s2+9)
· Evaluate the following inverse Laplace transform 2-1 S 5s + 3 ) 1 s2 + 4s +5% ] Solve the following system of differential equations S x' – 4x + y" | x' + x + y = 0, = 0. Use the method of Laplace Transforms to solve the following IVP y" + y = f(t), y(0) = 1, y'(0) = 1, where f(t) is given by J21 0, t>1. f(t) = {t, Ost<1, PIC.COLLAGE
Question 1: [25 pts] Consider the IVP y" – 4y' - 5y = 0, y(0) = 1, y0) = 2. a) Find the solution of the given IVP using the corresponding characteristic equation. b) Find the solution of the IVP using the Laplace Transform. c) Does the solution change if we would change the second initial condition as y'(0)=3? Explain.
Page 2 T Use the Laplace Transform method to solve the IVP 1-8y + 16y-te (0) = 1,0) = 4 Show all your work. Note: A partial fraction decomposition will not be needed here if you carefully solve for Y(s) = {v}(s), by first moving the expression of the form -as -b with a and b positive integers to the right hand side and then dividing both sides of the equation by the coefficient of Y(8) which will be of...
3. (a) (2 pts) Compute the inverse Laplace transform of the given function 2s+3 (b) (2 pts) Solve the IVP problem dy -y u2 (t)e-2(1-2), y(0) = 1 dt
1.Find the inverse Laplace transform 2. Use the method of variation of parameters to find the general solution of the system e -TTS F(s) = s(S2 + 1) x'= ( 2.)x+{2}') = Ax+ g(0)
Use the Laplace Transform method to solve the IVP y" - 8y + 16y = t4 y(0) = 1,5(0) - 4. Show all your work Note: A partial fraction decomposition will not be needed here if you carefully solve for Y(s) = {y}(s), by first moving the expression of the form -as - b with a and b positive integers to the right hand side and then dividing both sides of the equation by the coefficient of Y() which will...
Use the convolution theorem to find the inverse Laplace transform of the given function. 4 s' (s2 + 4) **** 14.30-0 $(2+4)
2. Use the Laplace transform to find a particular solution of the differen- tial equation (as explained in Example 2). After that, find the solution of the IVP. a) y"+y - 2y = 3t, y(0) = 0, '0) = 1 b) y" +4y=t, y(0) = 1, y(0) = 0
2. (a) Find Laplace transform of tecosht s2 - 65+7 (b) Find inverse Laplace transform of (52 – 4s +5)