Problem 7. PREVIEW ONLY -- ANSWERS NOT RECORDED (20 points) Use Laplace transforms to solve the...
(3 points) Use Laplace transforms to solve the integral equation y(t) -3 / sin(3v)y(t - v) dv - sin(t) The first step is to apply the Laplace transform and solve for Y(s) = L()(1) Y(s) = Next apply the inverse Laplace transform to obtain y(t) y(t) =
HW17: Problem 6 Previous Problem Problem List Next Problem (1 point) t Use Laplace transforms to solve the integral equation y(t) – 9 (t – v)y(v) dv = 6t. The first step is to apply the Laplace transform and solve for Y(s) = L(y(t)) Y(s) = Next apply the inverse Laplace transform to obtain y(t) y(t) =
Show work please (1 point) Use Laplace transforms to solve the integral equation y(t) – v yết – U) do = 4. The first step is to apply the Laplace transform and solve for Y(s) = L(y(t)) Y(s) = Next apply the inverse Laplace transform to obtain y(t) y(t) =
please help (1 point) Use the Laplace transform to solve the following initial value problem: y" + y = 0, y(0) = 1, y'(0) = 1 (1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(0), find the equation you get by taking the Laplace transform of the differential equation to obtain (2) Next solve for Y = (3) Finally apply the inverse Laplace transform to find y(t) y(t) =
Q4. Laplace Transforms a) (20 points) Solve the differential equation using Laplace transform methods y" + 2y + y = t; with initial conditions y(0) = y(O) = 0 |(s+2) e-*) b) (10 points) Determine L-1 s? +S +1
6. Solve an ODE Using Laplace Transforms: For this problem you are to use Laplace Transforms. Find the complete solution for the initial value problem yº+w2y = t +u.(t - Ttcost, y(0) = 1, y(0) = 0. Hint: Look carefully at the second forcing term and rewrite cost. You can solve this by brute force using the integral below. It would be a good exercise to make sure both approaches give the same Laplace transform. The integral The solution ſeat...
problem 7 Problem-4 [10 Points] Find the Laplace transforms of the functions in Figure. 2 Figure. 2: Triangular Function Problem-5 [10 Pointsl A system has the transfer function h(s) = (s1)(s +2) a) Find the impulse response of the system b) Determine the output y(t), given that the input is x(t) u(t) Problem-6 [10 Pointsl Use the Laplace transform to solve the differential equation +22+10v(t) 3 cos(2t) dt2 dt subject to v(0)-1, dv(O) Problem-7 [10 Points] Solve the integrodifferential equation...
In this exercise we will use the Laplace transform to solve the following initial value problem: y"-2y'+ 17y-17, y(0)=0, y'(0)=1 (1) First, using Y for the Laplace transform of y(t), i.e., Y =L(y(t)), find the equation obtained by taking the Laplace transform of the initial value problem (2) Next solve for Y= (3) Finally apply the inverse Laplace transform to find y(t)
(1 point) In this exercise we will use the Laplace transform to solve the following initial value problem: y" + 16 16, = { 10, 0<t<1 1<t , y(0) = 3, y'(0 = 4 (1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(t)), find the equation obtained by taking the Laplace transform of the initial value problem (2) Next solve for Y = (3) Finally apply the inverse Laplace transform to find y(t) y(t) =...
Previous Problem Problem List Next Problem (1 point) Use the Laplace transform to solve the following initial value problem: y" - y' – 12y = 0, y(0) = -7, y'(0) = 7 (1) First, using Y for the Laplace transform of y(t), l.e., Y = L(y(t)) find the equation you get by taking the Laplace transform of the differential equation to obtain =0 (2) Next solve for Y = A B (3) Now write the above answer in its partial...