Question 13 A particular solution of y + y'- 3x + 3 is None of the...
Question 12 Give the form of a particular solution of (4) – 4y + 13 y" – 36 y +36y=22* + sin(x) +5 given that r1 - 31 is a root of the characteristic equation. a) z-A 2+ + BCOS(x) + sin(x) +D b) c) z=A7** + Bx cos(3x) + Cx sin(3x) +D z=Ae2+ B cos(x) + C sin(x) +D z-A722* + B cos(x) + sin(x)+D z-A2+ Br 608(3x) + Cx sin(3x) +D d) e)
Question 11 Give the form of a particular solution of (4) – 16y-2 e 2x+3e" + cos2x) – 1 a) z-Axe* + Be **+Ccos(2x) + sin(2x) + E d) Axe 2+Be+Cx cos(2x) +Dx sin(2x) +B 3-Axe* +Be+3+ Cx cos(2x) +Dx sin(2x) + E 2=Axe 2+36-3x+cos(2x) + sin(2x) -Ae 2*+Be9*+ C'x cos(2x) + DX sin(2x) + E None of the above. e) f) Question 12 Give the form of a particular solution of J14) - 4 7 " +13 y" –...
1) Separate variables and find the particular solution of the differential equation x2 dy = y dx if y = 1 when x = 1. -1 - + 2 A) In y = =-- + 2 or y=e B) In y = ln x2 or y = x2 A) in y=- +2 or y=e**2 C) In y=-1+1 or w ts - +1 In y = -— +1 or y=e D) 4+2 or y= 2: 2) Find the general solution of...
1.- A) Calculate the value at x = 1/2 for the particular solution y(x) that meets the initial conditions y(0) = 0 and y'(0) = -1 of the ED (Use case I): y'' = 2 ( y')^2 B) Indicate the values of A and B so that y'' + Ay' + B y = 0 be the ED that has as a general solution to: y (x) = C1 cos (3x) e^3x + C2 sin (3x) e^3x
Find A PARTICULAR SOLUTION FOR CHINT: xz yu - 6x y' +4y= 3x"? (TRY ) y= Ax!/3 (6 fino A PARTICULAR SOLUTION FOR: y"-44'-12y = 22% (-3x2+4x+5) Hint : TRY y = 2 e2x THEN 205 € U= AX2+BX+C
You are given that yh = c1 cos(3x) +c2 sin(3x) is the general solution to the homogeneous differential equation y 00 + 9y = 0 (a) In each case below, write down your “guess” for the form of the particular solution to the differential equation. y 00 + 9y = f(x) Question 6. (Total marks: 14) You are given that y = cos(3x) + sin(3.c) is the general solution to the homogeneous differential equation y" +9y = 0 (a) In...
None of the above. Question 13 Use the Laplace transform to solve the initial-value problem: [y' + 2y -4 cos(5x), y(0)=2] 2) © plz) - cort5x) + 2 sin(52) + 5.24 1) 242 00452) + o) © Plz)= cos(x) + 2* sin(5x) – 60 6:20 d) y(x) =4 cos(5x) + 2 e) y(x) -4 cos(5x) - 2e2* 1) None of the above. Question 14
5. (5 points) a) Find a particular solution of y" +3y+4y 3x+2. b) Determine the appropriate form for a particular solution of y-4y- 2e* (2 points)
Question 20 The solution to the linear inequality − 10 x + 2 y > − 4 will be the half-plane lying a) on and below the solid line − 10 x + 2 y = − 4. b) below the solid line − 10 x − 2 y = − 4. c) above the dashed line − 10 x + 2 y = − 4. d) on and above the solid line − 10 x + 2 y = − 4. e) below...
4. Find the general and particular solution to the following: y' = 2xy + 3x? eh, y(0) = 5.