3 multiple choice questions Two solutions to a second order differential equation are linearly independent if...
Are the functions fi (x) = ex+4 and fz(x-er-5 linearly dependent or independent? A. Linearty dependent OB. Linearly independent Which of the following best describes the correct choice for part (a)? (Carefull) 0 A. Since the only solution to cfı + c/2 = 0 is ci = c2-0. B. Since the Wronskian equals zero for at least one x on (-o, o). C. Since the Wronskian never equals zero on (-oo, oo). D. Since the functions are scalar multiples of...
(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)...
Two linearly independent solutions of the differential equation y" - 6y' +9y = 0 are Select the correct answer La. V1 = em y=xe-3x b. V1 =ex, y =xe3x Lc. Vi=e- cosx, y =e-3x sinx d. Y1 =-3x, e. Yi = e3-cosx, yı = e3* sinx 22=xe-3x
(1 point) Solve the following differential equation by variation of parameters. Fully evaluate all integrals. y" +9y sec(3x) a. Find the most general solution to the associated homogeneous differential equation. Use c1 and c2 in your answer to denote arbitrary constants, and enter them as ct and c2. help (formulas) b. Find a particular solution to the nonhomogeneous differential equation y" +9y sec(3x). yp elp (formulaS c. Find the most general solution to the original nonhomogeneous differential equation. Use c...
The differential equation: A. Verify that yl-e* 1s a solution of the differential equation, B. Find a second solution, linearly independent. The differential equation: A. Verify that yl-e* 1s a solution of the differential equation, B. Find a second solution, linearly independent.
please give the correct answer with explanations, thank you Find a particular solution, yp(), of the non-homogeneous differential equation d2 y (2) +6 (de y(x)) +9y (x) = -12 , d22 given that yn (r) = A e-31+B 1 e 30 is the general solution of the corresponding homogeneous ODE. The form of yp() that you would try is Yp = ax + 6 yp = 2040 O yp=0x2-32 Enter your answer in Maple syntax only the function defining yp()...
Two linearly independent solutions of the differential equation y" - 5y' + 6y = 0 are Select the correct answer. a. Y1 = 62, y2 = 232 b. Y1 = 0 -6x, y2 = e** c. Y1 = e-Gx, y2 = et d. Y1 = 0-2, y2 = 2-3x e. Yi = e6x, y2 = e-*
Two linearly independent solutions of the differential equation y" + 4y' + 5y = 0 are Select the correct answer. a. Y1 = e-cos(2x), y2 = eʼsin (2x) b. Y1 = e-*, y2 = e-S* c. Yi= e-*cos(2x), y1=e-* sin(2x) d. Y1 = e-2xcosx, x, y2 = e–2*sinx e. Y1 = e', y2 = 5x
A third-order homogeneous linear equation and three linearly independent solutions are given below. Find a particular solution satisfying the given initial conditions. y (3) + 2y" - y' - 2y = 0; y(0) = 7, y' (0) = 16, y''O) = 0; e y2 = e-X, y3 = e - 2x Y The particular solution is y(x) = .
A third-order homogeneous linear equation and three linearly independent solutions are given below. Find a particular solution satisfying the given initial conditions. yl) + 2y'' – y' - 2y = 0; y(0) = 2, y'(0) = 12, y''(0) = 0; Y1 = ex, y2 = e -X, y3 = e - 2x The particular solution is y(x) = .