Use variation of parameters to find a particular solution to the given DE -3pt 11.)y" - 2y'+y- tet 13.) y'', + 4y'--8 [cos (2t) + sin(2t)] 15.) хту-xy' + y = x3 6e Use variation of parameters to find a particular solution to the given DE -3pt 11.)y" - 2y'+y- tet 13.) y'', + 4y'--8 [cos (2t) + sin(2t)] 15.) хту-xy' + y = x3 6e
7. Given that y(x) = sin 2x is a particular solution to y" + 2y + 4y - 4 cos 2x = 0, find the general solution.
1. Find the general solution to the equation y" - y - 2y = -e- 2. Find a particular solution to y" + 4y = 11 sin(2t) + cos(2t) 3. Find the form of a particular solution to be used in the Method of Undetermined Coefficients for the equation y" + 2y' +2y = te-* cost Do not solve the equation
#32 U. + 2y + y + 1 -e: y(0) = 0, y'(o) - 2 In Problems 31-36, determine the form of a particular solution for the differential equation. Do not solve. 31. y" + y = sin : + i cos + + 10' 32. y" - y = 2+ + te? + 1221 x" - x' - 2x = e' cos - + cost y" + 5y' + 6y = sin t - cos 2t 35. y" –...
Find the general solution or particular solution of each the following DE's 1) (y-y2 tanx)dx + (2y+tanx)dy=0 2) (x2+y2+x)dx + xydy-0 i y(-1)-1 4) For the initial value problem y' + xy - xy? ex2 ; y(0)-1 Find the explicit solution if y>0 dy dae dy
y''-3y'-4y=0 has a general solution y=C1e^(4x)+C2e^(-x) find the particular solution if it exists for y(0)=0 & y(1)=2
3. Find a particular solution of y" + 3y' + 4y = 28x e2x 3. Find a particular solution of y" + 3y' + 4y = 28x e2x
Use undetermined coefficients to find the particular solution to y''+2y'−3y=4e^−3t
Q4 please 4. (a) Find the general solution of the equation y" +2y +2y tan by varia- tion of parameters 6 marks] (b) Find a particular solution of the equation y" +2/ +2y = sin 2x by method of undetermined coeficients. 4 marks] (c) Use Laplace transform to solve the initial value problem l-1, 21 0-,0)- [10 marks] 4. (a) Find the general solution of the equation y" +2y +2y tan by varia- tion of parameters 6 marks] (b) Find...
5. (5 points) a) Find a particular solution of y" +3y+4y 3x+2. b) Determine the appropriate form for a particular solution of y-4y- 2e* (2 points)