(27 points) Find the general solution of the associated homogeneous equation for each nonhomogeneous differential equation...
(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. (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" – 9y' - 22y = 5xe -2x (b) (10 points) y" - 4y + 29 y = 8xsin 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
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
(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...
For each nonhomogeneous linear equation below, determine what the guess solution yp would be for the method of undetermined coefficients. with steps! Thank you (a) y′′ − 4y′ + 13y = 80e−3t (b) y′′−6y′+9y=(t+1)e3t (c) y′′+4y=sin(2t)+t3−1 (d) 4y′′ − 4y′ + y = 16et/2
(1 point) a. Find a particular solution to the nonhomogeneous differential equation y" + 3y - 10y = ex. yp = help (formulas) b. Find the most general solution to the associated homogeneous differential equation. Use cy and c2 in your answer to denote arbitrary constants, and enter them as c1 and c2. Yh = help (formulas) c. Find the most general solution to the original nonhomogeneous differential equation. Use cy and C2 in your answer to denote arbitrary constants....
(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)...
Find the general solution of the following 2nd order linear nonhomogeneous ODEs with constant coefficients. If the initial conditions are given, find the final solution. Apply the Method of Undetermined Coefficients. 7. y" + 5y' + 4y = 10e-3x 8. 10y" + 50y' + 57.6y = cos(x) 9. y" + 3y + 2y = 12x2 10. y" - 9y = 18cos(ix) 11. y" + y' + (? + y = e-x/2sin(1x) 12. y" + 3y = 18x2; y(0) = -3,...