6. Find the particular part of the solution of the difference equation y(n+2) – 2y(n+1)+y(n) =...
Let f(x,y) = cx( 1-y), 0 < x < 2y < 1, zero elsewhere. a) Find c. b) Are X and Y independent? Why or why not? c) Find PX +Y05)
(1 point) Let x and y have joint density function p(2, y) = {(+ 2y) for 0 < x < 1,0<y<1, otherwise. Find the probability that (a) < > 1/4 probability = (b) x < +y probability =
Problem 2: [Also challenging] Find the solution of the following IVP: y' +2y = g(t), with y(0) = 3 where g(t) = - 0<t<1: g(t) = te-2 > 1.
2. (20 points) Find the solution y (t) of the following differential equation: -{ 0t< 4 0 y"9y (t) y(0) = 1, /(0) = 0, t 4 3
Suppose that f (x II 2y), 0 < x < 1,0 < y < 1. Find EX + Y).
2 a) Find the particular solution for y' - 2y' + y = 6e' b) Find y, for y' + 3y' - 36x² + 8e-> JT JT c)Find the general solution y(x) = y, + Ay, (x) + Byz(x),and solve IV y + 4y = 2 sin2t, y
Q4 please 4. (a) Find the general solution of the equation y" +2y +2y tan by varia- tion of parameters 6 marks] (b) Find a particular solution of the equation y" +2/ +2y = sin 2x by method of undetermined coeficients. 4 marks] (c) Use Laplace transform to solve the initial value problem l-1, 21 0-,0)- [10 marks] 4. (a) Find the general solution of the equation y" +2y +2y tan by varia- tion of parameters 6 marks] (b) Find...
If X and Y have a joint probability density function specified by 2-(+2y) find P(X <Y).
a) Find the general solution of the differential equation Y'(B) + 2y(s) = (1)3 8>0. b) Find the inverse Laplace transform y(t) = --!{Y(s)}, where Y(s) is the solution of part (a). c) Use Laplace transforms to find the solution of the initial value problem ty"(t) – ty' (t) + y(t) = te", y(0) = 0, y(0) = 1, fort > 0. You may use the above results if you find them helpful. (Correct solutions obtained without Laplace transform methods...
The difference equation y(n+2) -3y(n+1)+2y(n) = 1 for n 20 has initial conditions y(0)= -1 and y(1) 1 1. Find the value of y(3) using iteration. (a) Find the particular solution of y(n) (b) Find Y(z). (It should only be expressed as the ratio of two polynomials) (c) The difference equation y(n+2) -3y(n+1)+2y(n) = 1 for n 20 has initial conditions y(0)= -1 and y(1) 1 1. Find the value of y(3) using iteration. (a) Find the particular solution of...