The general solution of the equation y 9y = 0 is y cicos(3x) C2sin(3x). Find values...
please help The general solution of the equation y4y 0 is y = ccos(2x)c2sin(2x) Find values of ci and c2 so that y(0) and y (0) 8 -3 C1 = C2= Plug these values into the general solution to obtain the unique solution y = The general solution of the equation y4y 0 is y = ccos(2x)c2sin(2x) Find values of ci and c2 so that y(0) and y (0) 8 -3 C1 = C2= Plug these values into the general...
Find the general solution, y(t), of the differential equation t y" – 5ty' +9y=0, t> 0. Below C1 and C2 are arbitrary constants.
The general solution of y(1) – 5y" – 36y = 0) is: (a) y = Cicos 3x + C2 sin 3x + C3e2x + C4e-20 (b) y=Ci cos 3x + C2 sin 3x + C3 cos 2x + C4 sin 2.0 (e) y=Cicos 2x + C2 sin 2x + C3e3x + Cae-31 (d) y=Cicos 2x + C2 sin 2x + C3e3x + Caxe3r (e) None of the above.
(8 pts) In this problem you will solve the non-homogeneous differential equation y" + 9y = sec (3x) (1) Let C and C2 be arbitrary constants. The general solution to the related homogeneous differential equation y" + 9y = 0 is the function yn (x) = C1 yı(2) + C2 y2(x) = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(x) + C2g(x) + C19(x) + C2 f(x). (2) The particular solution yp(x)...
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...
a. Find a particular solution to the nonhomogeneous differential equation y" + 16y = cos(4x) + sin(4x). Yo = (xsin(4x))/8-(xcos(4x))/8 help (formulas) b. Find the most general solution to the associated homogeneous differential equation. Use ci and C2 in your answer to denote arbitrary constants. Enter c1 as c1 and C2 as c2. Un = c1cos(4x)+c2sin(4x) help (formulas) c. Find the solution to the original nonhomogeneous differential equation satisfying the initial conditions y(0) = 3 and y'(0) = 2. y...
II. Determine the general solution of the given 2nd order linear homogeneous equation. 1. y" - 2y' + 3y = 0 (ans. y = ci e' cos V2 x + C2 e* sin V2 x) 2. y" + y' - 2y = 0 (ans. y = C1 ex + C2 e -2x) 3. y" + 6y' + 9y = 0 (ans. y = C1 e 3x + c2x e-3x) 4. Y" + 4y = 0, y(t) = 0, y'(T) =...
Find the general solution of the equation y" + 361y = 0. y(t) = C1 cos 19t + c2 sin 19t o o o o y(t) = ci cos t-cı sin t y(t) = ci cos t+ c2 sin 19t y(t) = cı cos 19t+ c2 sin t
(5 points) Find the general solution to the differential equation y" – 2y + 17y=0. In your answer, use Cį and C2 to denote arbitrary constants and t the independent variable. Enter Cų as C1 and C2 as С2. y(t) = help (formulas) Find the unique solution that satisfies the initial conditions: y(0) = -1, y'(0) = 7. y(t) =
(4) Consider the IVP 9y" + 6y' +2y = 0, y(37) = 0, y/(3x) = }: a) Determine the roots of the characteristic equation. b) Obtain the general solution as linear combination of real-valued solutions. c) Impose the initial conditions and solve the initial value problem.