(8pts) Determine if {e*, e 2x} form a basis for the solution space of the differential...
Determine the form of a particular solution for the differential equation. Do not solve. y" - 4y' + 5y = e 7 + t sin 6t - cos 6t The form of a particular solution is yp(t)- (Do not use d, D, e, E, I, or I as arbitrary constants since these letters already have defined meanings.)
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. 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
Determine the form of a particular solution for the differential equation. Do not solve. y"-y=4e2 +772e2 The form of a particular solution is yp(t) = 0 (Do not use d, D, e, E, I, or I as arbitrary constants since these letters already have defined meanings.)
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
Using the Method of Undetermined Coefficients, determine the form of a particular solution for the differential equation. (Do not evaluate coefficients.) y" - 4y + 4y = 8621 What are the roots of the auxiliary equation associated with the given differential equation? The associated auxiliary equation has the two roots OA. (Use a comma to separate answers as needed) OB. The associated auxiliary equation has the double root OC. There are no roots to the associated auxiliary 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
(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
Solve the following differential equation. Do not use Laplace. y'' – 4y' = 2e (2x+3) - Write the corresponding homogeneous equation and find the homogeneous solution. - Find the particular solution using the non-homogeneous differential equation. - Finally write the general solution.
Determine the form of a particular solution for the differential equation. Do not solve. y" - 18y' + 82y = et + tsin 2t - cos 2t The form of a particular solution is yp(t)= (Do not use d D. e. Ei or las arbitrary constants since these letters already have defined meanings.)