02 Solve the Fredholm integral equation of the second kind y(x)-f(x) +AJ0x(1 H) y(t) dt when...
02 Solve the Fredholm integral equation of the second kind 3. y(x) fx)+A( ) y(t) dt when A is not an eigenvalue 4. Q2 Find the Jordon canonical for of A -3 8 3 4 -8-2 02 Solve the Fredholm integral equation of the second kind 3. y(x) fx)+A( ) y(t) dt when A is not an eigenvalue 4. Q2 Find the Jordon canonical for of A -3 8 3 4 -8-2
1 o1Express the differential equation y"(x) -y(x) -6y x 1 with y(0) y(1) -0 into Fredholm integral equation. 2, a2 Solve the Fredholm integral equation of the second kind: y(x)-t(x) +Nox(1 +t) y(t) dt when λ is not an eigenvalue .
1. Solve each of the following inhomogeneous Fredholm integral equations of the second kind for all values of 1 for which there is a solution. (x) = cos x + 2 sin x pt)dt ел Jo
Consider the Fredholm integral equation u (t) sin (t u(s) ds+f(t), where co Rand f eC 10,1]. Determine a range of co for which the integral equation admits a unique solution. Consider the Fredholm integral equation u (t) sin (t u(s) ds+f(t), where co Rand f eC 10,1]. Determine a range of co for which the integral equation admits a unique solution.
(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...
Solve for y(t). dy/dt + 2x = et dx/dt-2y= 1 +t when x(0) = 1, y(0) = 2
Problem 4: Evaluation of the convolution integral too y(t) = (f * h)(t) = f(t)h(t – 7)dt is greatly simplified when either the input f(t) or impulse response h(t) is the sum of weighted impulse functions. This fact will be used later in the semester when we study the operation of communication systems using Fourier analysis methods. a) Use the convolution integral to prove that f(t) *8(t – T) = f(t – T) and 8(t – T) *h(t) = h(t...
3. (25 Points) Find f(t). f(0) + f(t - 1)f(t)dt = t. Hint: The second term on the left side is a convolution and it might be helpful to use the Laplace Transform. 1 4. (10 Points) Solve the initial value problem by Laplace transform techniques. x" + 5x' + 4x = 0;x(0) = 1,x'(0) = 0. I 5. (15 Points) Find a series solution for the following differential equation. Calculate the radius of convergence. 2(x - 1)y' = 3y...
Solve the given integral equation or integro-differential equation for y(t). yʻce) + f(t-v1yv) dv = 4t, y(0)=0 y(t)
Solve the given integral equation or integro-differential equation for y(t). t y't) + f(t– vy(v) dv=4t, y(0) = 0 0 y(t) =