Find the general solution of the DE: y’’(x) + 6y’(x) + 8y(x) = 3e^(-2x) + 2x
B5. Find the general solution of x' = 2x + 6y + et y' = x + 3y – e'.
3) Find the solution to y" -6y' +8y=16 x(0)=0, x'(0)=0 given that y.(x) = ce?* +cze** and y, (x) = 2.
Find the general solution of y'' + y'-6y=(9x-2)e^(2x). (Use the method of undetermined coefficients) Please show all work and steps! 2. Find a general solution of y" + y' - 6y = (9.C -- 2)e2.. (22 p'ts, use the method of undeter- mined coefficients.)
1. Given that y, - e is a solution of (2x-x') y" +(x-2) y'+2(1-x) y. a. Find the general solution on the interval (2, o). y(3)-1 b. Find a solution of the DE satisfying ¡y(3):0 1. Given that y, - e is a solution of (2x-x') y" +(x-2) y'+2(1-x) y. a. Find the general solution on the interval (2, o). y(3)-1 b. Find a solution of the DE satisfying ¡y(3):0
use variation of parameters to find a particular solution yp(x) y" + 6y + 8y = e2x dx + y2() San f(x)y2(x) f(x)yı(2) Recall that, yp(x) = -41(x) dr. aW(41, 42) aW(41, 42) If you use the method of undetermined coefficients you will receive zero credit.
(10 point) Solve the following initial value problems. a) y"+ 4y' + 8y = 40cos(2x), y(0) = 8, y'(0) = 0 b) y" + 6y' + 13y = 12e-3xsin(2x), y(0) = 0, y'(0) = 0 (10 point) Find a general solution of each of the following nonhomogeneous equations. a) y" + 4y = 12x−8cos(2x) b) y(4)− 4y" = 16+32sin(2x)
- 3e - sin(-5x) Find lim - 2x (x,y)+(0,0) -3e - sin(-5x) lim - 2x (x,y)-(0,0) (Type an integer or a simplified fraction.)
Find the general solution of the given differential equation. y" - 6y' + 6y = Here y(t) =
Find the general solution to y'' + 8y' + 41y = 0. Give your answer as y=.... In your answer, use c1 and c2 to denote arbitrary constants and the independent variable.
Find a general solution to the differential equation. y'' – 6y' +9y=t-5e3t The general solution is y(t) =