(1 point) Consider the IVP У + 3ty — бу %3D 3, у(0) — 0, У (0) — 0 (a) What is the Laplace transform of the differential equation, after being put into standard form? Y'(s) ) Y(s) = |(b) What is the solution to the differential equation? y(t)
шiлili b, y + бу 0; у(0) 0, (0) 1; 4y" + 5 -- 2y o Problem 4. Sоlvе hоtоgenous epuations
Solve the initial value problem dy + бу da 0, y(In 4-4.
5) Consider the IVP у"F-у, + 2У = 5x,y(0)= 4, y'(0) =-4. 5) Consider the IVP у"F-у, + 2У = 5x,y(0)= 4, y'(0) =-4.
Find the solution of the initial value problem [y(0)=-1, у"(0)=-3, у "(0)=0, у"(0)-0] a) y--3-х -2x-2x f None of the above.
У"-у,_6y 8. y'(0)-0 -cost y(0)-0 9. y"-y,-6y-3 sin2t y'(0) y(0)-1 0
Let X and Y be random variables with joint density function f(x,y) бу 0 0 < y < x < 1 otherwise The marginal density of Y is fy(y) = 3y (1 – y), for 0 < y < 1. True False
SOLVE #3 AND #4 PLEASE Use the Laplace transformation to solve the IVP. 1. y"-6y' + 9y-24-9t, y(0)-2, y, (0)-0 2. 9y" - 12y'4y50ey(0)--1,y'(0)2 3. У"-2y'--. 1 2 cos(2t) + 4 sin(2t),y(0)-4,y'(0)-0 Use the Laplace transformation to solve the IVP. 1. y"-6y' + 9y-24-9t, y(0)-2, y, (0)-0 2. 9y" - 12y'4y50ey(0)--1,y'(0)2 3. У"-2y'--. 1 2 cos(2t) + 4 sin(2t),y(0)-4,y'(0)-0
QUESTION 4 Consider the CDF 0 у<0 0.5 F(y) = 0.75 0.90 Osy<2 2sy<3 3sy<5 1 Y>5 Find pſy=5) O A. 0.10 B. 0.15 C. 0.25 D.0.25 QUESTION 5 Consider the PM.F
Question 3 (30 Marks) Use the Laplace transform to solve the following initial value problems y' -y 2cos5t, у,-у-2cosSt, with initial condition y(0)0 with initial condition y(0) 1,y' (0)-1.