(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-...
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)
use the Laplace transform to solve the given system of differential equations dx dt dx dt dt dt x(0) 0, y(o)0 x(t) =
3. Let the Laplace transforms of signals (t) and y(t) be X(s) and Y(s) with appropriate regions of convergence, respectively (a) Show that the Laplace transform of x(t) * y(t) is X(s)Y (s). What is the region of convergence? (b) Show that the Laplace transform of tx(t) is -dX(s)/ds with the same region of x(t) convergence as tn-1 1 for Re{sa} > 0. -at e (c) Show that the Laplace transform of 'u(t) is n 1)! (sa)" 1 for Refsa}...
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.
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) =
4) Solve for x(t)n using Laplace transform: dx dt + 2x = 6 where x(0)=-5 Highlight the transient responce
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.
II. Answer the following questions concerning the simultaneous differential equa- dac tions below. Here, à dt dr -2- 3y 2, dt dt2 dy da (2) 2y, dt df x(0)0, (0)0, y(0) = 2. -- 1. Let us transform the simultaneous differential equations in Eq.(2) into. da Ax b, (0) dt Here ais defined as the form x(t) (t) y(t) x(t) (3) A is a constant matrix, and b and c are constant vectors. Obtain A, b and c Calculate all...
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt 7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
use Laplace transforms to solve the given system of differential equations ponts) 6)) Use Laplace transforms to solve the system dc y = 2x-2y dt.dt dx _ ay = x - y dt at x(O) = 1, y(0) = 0