The functions (t), y(t) satisfy the system of equations dt d v052(01(0 3y(t) and the initial...
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) =
(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...
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 Laplace transform of y(t) Your answer should be expressed as a function of s using the correct syntax.
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.
slove the system eqution: d^3y(t)/dt^3 - 2 d^2y(t)/dt^2 - 5 dy(t)/dt +6 y(t) = 2 d^2u(t)/dt^2 +du(t)/dt +u(t) A) compute the transfer function Y(s)/U(s)? B)Find inverse Laplace for y(t) and x(t)? C) find the final value of the system? D)find the initial value of the system? Please solve clearly with steps.
Solve the system of equations with Laplace Transforms: (differential equations) all parts please Solve the system of equations with Laplace Transforms: x' + y' = 1, x(0) = y(0) = x'(0) = y'(0) = 0. y" = x' Let X(s) = LT of x(t) and Y(s) = LT of y(1). First obtain expressions for X(s) and Y(s) and list them in the form ready for obtaining their inverses. a. Y(s) = X(s) = %3D b. Now obtain the inverse transforms....
Solve the system of differential equations dx/dt = x-y, dy/dt = 2x+y subject to the initial conditions x(0)= 0 and y(0) = 1.
Consider the initial value problem y" +3y' +2y = (t-1)+r(t), y(0) = y(0) = 0, where 8(t-1) is Dirac's delta function and S4 if 0<t<1 r(t) 8 if t > 1 (a) Represent r(t) using unit step functions. (b) Find the Laplace Transform of 8(t-1)+r(t). (c) Solve the above initial value problem. {
3. Suppose x,y,z satisfy the competing species equations <(6 - 2x – 3y - 2) y(7 - 2x - 3y - 22) z(5 - 2x - y -22) (a) (6 points) Find the critical point (0,Ye, ze) where ye, we >0, and sketch the nullclines and direction arrows in the yz-plane. (b) (6 points) Determine if (0, yc, ze) is stable. (c) (8 points) Determine if the critical point (2,0,0) is stable, where I > 0.
Sheet1 Control 1. Solve the following differential equations using Laplace transforms. Assume zero initial conditions dx + 7x = 5 cos 21 di b. + 6 + 8x = 5 sin 31 dt + 25x = 10u(1) 2. Solve the following differential equations using Laplace transforms and the given initial conditions: de *(0) = 2 () = -3 dx +2+2x = sin21 di dx di dx di 7+2 x(0) = 2:0) = 1 ed + 4x x(0) = 1:0) =...