QUESTION 3 Determine whether the differential equation homogeneous and find its general solution....
Find the general solution of the following non-homogeneous differential equation d 2 y dt2 + 2 dy dt + y = sin (2t). (2) Now, let y(t) be the general solution you find, when happen if we take lim t→+∞ y(t)? 2. Find the general solution of the following non-homogeneous differential equation dy dy sin (2t) (2) 2 +y= dt dt2 Now, let y(t) be the general solution you find, when happen if we take lim y(t)? t-++oo
3. Find the general solution of the homogeneous differential equation. x y = xºy - 4y
4. Consider the differential equation +2y + 2y = cost (a) (5 points) Find the general solution to the corresponding homogeneous equa- tion. (b) (5 points) Find a particular solution, y(t), to the non-homogeneous equation. (c) (2 points) Determine the general solution to the non-homogeneous equation.
5. Find the general solution to the following non-homogeneous differential equation. x" – 2x' + x = t2 +t+1
QUESTION 7 A solution of a homogeneous differential equation with constant coefficient is given by y = Ae-3* +Bsin 4x +Ccos 4x. Determine the a) order and the roots of the equation. (3 marks) b) differential equation. (3 marks)
(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
Problem 1 (14 points) (a) Find the general solution to a third-order linear homogeneous differential equation for y(1) with real numbers as coefficients if two linearly independent solutions are known to be e-21 and sin(3.c). e (b) Determine that differential equation described in part (a).
Problem 1 (14 points) (a) Find the general solution to a third-order linear homogeneous differential equation for y(1) with real numbers as coefficients if two linearly independent solutions are known to be e-21 and sin(3.c). e (b) Determine that differential equation described in part (a).
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