x(t) and y(t) satisfy the following system of differential equations: di +827-y=0, +3y=e-4t, x(0)=y(0)=0. Find the...
x(t) and y(t) satisfy the following system of differential equations: de todo-y=0, de+ 5y =e-6t, sc(0)=y(0)=0. Find the Laplace transform of y(t) Your answer should be expressed as a function of s using the correct syntax.
The functions (t), y(t) satisfy the system of equations dt d v052(01(0 3y(t) and the initial conditions (0)1 and y(0)4 Suppose that the Laplace transforms of z(t), y(t) are respectively X(s), Y(8). By forming algebraic equations in X(s), Y(8). find and the enter the function X(s), Y(8) below syntax. X(s) Y(s)
(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-ay (0)-0, and ax (0)-λ. Here n, μ, and λ are all positive real numbers. This problem involves Laplace transforms, has three parts, and is continued on the next page. You must use Laplace transforms where instructed to receive credit for your solution (a). Define the Laplace Transforms X(s) -|e"x(t)dt and Y(s) -e-"y(t)dt Laplace Transform the differential equations for x(t) and y(t) above, and incorporate...
The functions æ(t), y(t) satisfy the system of equations x (t) = -3 x (t) – y(t) ft y(t) = 5 x (t) – y(t) and the initial conditions x(0) = 1 and y(0) = -1. Suppose that the Laplace transforms of x(t), y(t) are respectively X(s), Y(s). By forming algebraic equations in X(s), Y(s)., find and the enter the function X(s), Y(s) below in maple syntax. X(s) = Y(s) =
what is the Laplace transform ot J(t)=H(t-7)8te6t? Your answer should be expressed as a function of s using the correcd syntax Laplace transform is F(s) What is the Laplace transform of 12 sinh(2t) Your answer should be expressed as a function of s using the correct syntax Laplace transform is F(s) what is the Laplace transform ot J(t)=H(t-7)8te6t? Your answer should be expressed as a function of s using the correcd syntax Laplace transform is F(s) What is the Laplace...
2. (10 pts) Given the following differential equations, find the total response y(t) if y(0) = 1 for the input x(t) = 24 cos(6t) u(t) by using Laplace Transform. how t6yce) = . _ x06) y(t) =
(1 point) Consider the following initial value problem: 4t, 0<t<8 \0, y" 9y y(0)= 0, y/(0) 0 t> 8 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 and solve for Y(s)
1. Solve the system of equations using Laplace Transform(LT): With IV: x(0) 4 With IV :y (0)-5 a. Apply Laplace transform (LT) to the system and solve, by using elimination method, for x(s), and y(s). b. Apply inverse-Laplace transform (L:'T) to the system of s-functions, then solve for x(t), and y(t) 1. Solve the system of equations using Laplace Transform(LT): With IV: x(0) 4 With IV :y (0)-5 a. Apply Laplace transform (LT) to the system and solve, by using...
6 (5) Solve the differential equation using a Laplace Transform: y 3y' +2y t y(0) 0, y'(0) 2
differential equations Use the Laplace transform to solve the given initial-value problem. y' + 3y = et, y(0) = 2 y(t) =