The correct option is (e). The explanation is as follows:
Find the homogeneous equation with constant coefficients of least order that has the following as a...
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,...
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) =...
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) = .
1. Consider the differential equation: 49) – 48 – 24+246) – 15x4+36” – 36" = 1-3a2+e+e^+2sin(2x)+cos - *cos(a). (a) Suppose that we know the characteristic polynomial of its corresponding homogeneous differential equation is P(x) = x²(12 - 3)(1? + 4) (1 - 1). Find the general solution yn of its corresponding homogeneous differential equation. (b) Give the form (don't solve it) of p, the particular solution of the nonhomogeneous differential equation 2. Find the general solution of the equation. (a)...
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) = .
Given the Homogeneous Linear Differential Equations with Constant Coefficients, determine the general solution y(v) + 4y(iv) + 5y“” – 6y' – 4y = 0 y(x) = cte* + c2e-2x + c4e +04e-* + e-* (c4Cos x + C5 Sen x) Answer:
please help me solve #1,2,3 !!! greatly appreciated (2.2 Homogeneous linear equations with constant coefficients 1. Find a fifth-order homogeneous linear differential equation with constant coefficients whose general solution is y = (1 + Cze* + czxe* + e-*(C4cos2x + cssin2x). 2. Solve 2y'' – 3y" – 8y' – 3y = 0. 3. Solve y" + y' + y = 0.
3. (10 points) Suppose that an nth-order homogeneous ODE with constant coefficients has the following general solution y = Ge-*+ C2 cos x + C3 sin x + Cex cos x + C5xsin x + C + Cyx. What is n? What are the roots of the characteristic equation of this ODE? What is the characteristic equation? What is the ODE?
(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
(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