1. (5 points) Use a Laplace transform to solve the initial value problem: y' + 2y...
(4 points) Use the Laplace transform to solve the following initial value problem: y" – 2y + 5y = 0 y(0) = 0, y'(0) = 8 First, 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 = 01 Now solve for Y(3) By completing the square in the denominator and inverting the transform, find g(t) =
Use the Laplace transform to solve the initial value problem: y" - 3y' + 2y = 4t + ezt, y(0) = 1, y'(0) = -1
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)
17. Use the Laplace transform to solve the initial value problem: y" + 4y' + 4y = 2e-, y(0) = 1, (O) = 3. 18. Use the Laplace transform to solve the initial value problem: 4y" – 4y + 5y = 4 sin(t) – 4 cos(1), y(0) = 0, y(0) = 11/17.
Use the Laplace transform to solve the given initial-value problem. Use the table of Laplace transforms in Appendix III as needed. y" + 25y = f(t), y(0) = 0, y (O) = 1, where RE) = {cos(5€), Ostan (Σπ rce) = f sin(51) + (t-1) -sin 5(t-T) 5 Jault- TE ) X
B) Use the Laplace transform to solve the given initial-value problem: y' + 2y = 2cos(2+), with y(0) = 1
Solve the following initial value problem using the method of Laplace transform. y" + 2y' +10y = f(t); y(0)= 1, y'(0) = 0, where, f(0) = 10, Ost<10, 20, 10<t.
Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y'' + 2y = 2t4, y(0) = 0, y'(0) = 0 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Y(s) = Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" -7y' + 12y = 3t e 3t, y(0) = 4, y'(0) = -1 Click...
(1) Use the Laplace transform method to solve the initial value problem x + 2y. V=x+', (0) = 0 (0) -0. (Note that once you find either (t) or y(t), the other can be computed from the syste of ODE.) ISA - X-xo) = x +2Y ST-y(0) = X te 15.- 2 1 X(5-)-2Y=0 lo -2ts(s)
(t)= . Use the Laplace transform to solve the following initial value problem: 44" + 2y + 18y = 3 cos(3+), y(0) = 0, y(0) = 0. a. First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation and then solve for L{y(t)}. Do not perform partial fraction decomposition since we will write the solution in terms of a convolution integral. L{y(t)}(s) b. Express the solution y(t) in terms of a...