2. (27 points) Find the general solution of the associated homogeneous equation for each nonhomogeneous differential...
(27 points) Find the general solution of the associated homogeneous equation for each nonhomogeneous differential equation below. Then determine the form of a particular solution y, of the nonhomogeneous equation. Do not solve for the undetermined coefficients in yp: (a) (10 points) y" - 9y' - 22y = 5xe-2x (b) (10 points) y" – 4y' + 29 y = 8x sin 3x
(27 points) Find the general solution of the associated homogeneous equation for each nonhomogeneous differential equation below. Then determine the form of a particular solution ур of the nonhomogeneous equation. Do not solve for the undetermined coefficients in yp (a) (10 points) y" – 9y' – 22 y = 5xe -2x (b) (10 points) y" – 4y' + 29 y = 8x sin 3x
#2 part a b and c please. please write solutions neatly 2. (27 points) Find the general solution of the associated homogeneous equation for each nonhomogeneous differential equation below. Then determine the form of a particular solution y, of the nonhomogeneous equation. Do not solve for the undetermined coefficients in y, (a) (10 points) y" - 9 - 22 y 3x2 (b) (10 points) y" - 4y' + 29y = 8r sin 3x 3 2. (c)points) Find a homogeneous linear...
a. Find a particular solution to the nonhomogeneous differential equation y" + 4y = cos(2x) + sin(2x) b. Find the most general solution to the associated homogeneous differential equation. Use cand in your answer to denote arbitrary constants. c. Find the solution to the original nonhomogeneous differential equation satisfying the initial conditions y(0) = 8 and y'(0) = 4
5. (10 points) Find the general solution of the following differential equations. 4y"-12y'+9y = 0 (0) = 2 y'(0) = 5 6. (10 points) What would be the form of the particular solution of y'"+y" e' + cost-21 using the method of undetermined coefficients. DO NOT SOLVE
Question Three: (7 marks) (a) Find the general solution of the following homogeneous equation. (b) Apply the method of Undetermined Coefficients to write ONLY the form of the particular solution of the following nonhomogeneous equation "-2y+5y 24re* cos(2x). Question Three: (7 marks) (a) Find the general solution of the following homogeneous equation. (b) Apply the method of Undetermined Coefficients to write ONLY the form of the particular solution of the following nonhomogeneous equation "-2y+5y 24re* cos(2x).
Find the general solution of the given second-order differential equation. y'' + 10y' + 25y = 0 Solve the given differential equation by undetermined coefficients. y'' + 4y = 2 sin 2x Solve the given differential equation by undetermined coefficients. y'' − y' = −10
3. (17 points) Find the general solution of the linear differential equation y" + 5y + 4y = (3x - 8)e* using the method of undetermined coefficients.
1. Second order ODE (25 points) a. Consider the following nonhomogeneous ODEs, find their homogeneous solution, and give the form (no need to determine coefficients) of nonhomogeneous solution. (12 points) i. 44'' + 3y = 4x sin ( *2) ii. J + 2 + 3 = eº cosh(22) b. Find the general solution of y" + 2Dy' + 2D'y = 5Dº cos(Dx) where D is a real constant with following steps i) Determine homogeneous solution, ii) Find nonhomogeneous solution with...
(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...