(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)
(10 point) Solve the following initial value problems. a) y"+ 4y' + 8y = 40cos(2x), y(0)...
Problem 1: Solve the initial value problems: a 2y" – 3y' +y=0 y(0) = 2, 7(0) = 1 by' + y - 6y = 0 y(0) = -1, y'(0) = 2 cy' + 4y + 3y = 0 y(0) = 1, y'(0) = 0 Problem 2: Solve the initial value problems: a y' +9y = 0 y(0) = 1. 1'(0) = -1 by" - 4y + 13y = 0 y(0) = 1, y'(0) = 3 cy" + ly + ly...
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
Mathematical Physics 2 H.W.4 y"+y-6y y+4y+4y y"+y0 y(0) 2 and y '(0) Subject to the initial conditionns 1 y"-y0 y(0) 2 and y'(0) = 1 Subject to the initial conditions yy'-12y 0 y(0) 2 and y '(0) 1 Subject to the initial conditions y"-4y xe Cos2x y"-2y'x+ 2e y"+y=sinx "-4y'+13y= e cos3x Solve the boundary-value problem y(0) = 1 and y(1) = 3 y"+ 2y'+y=0 Solve the initial-value differential equation y"+ 4y'+4y=0 subject to the initial conditions y (0) =...
solve for x and y, linear equations using the elimination method 2x+6y=-2 5x-3y=3 and -9x+3y=5 9x+4y=-6 is the following system dependentinconsistent or does it have a unique solution? why is this so? x-8y=9 6x-48y=36
8. Solve the following initial value problem: y" - 6y' + 13y = 0, y(a) = b, y'(c) = d (Note: a, b,c,d will be an a=1 b=7 c=8 d=9]nt ID number)
Solve the initial value problem 2x+y-bxy'+4y=0 Y()=0 ; y'C1=252
y"+ 2y' + y = 0, y(0) = 1 and y(1) = 3 Solve the initial-value differential equation y"+ 4y' + 4y = 0 subject to the initial conditions y(0) = 2 and y' = 1 Mathematical Physics 2 H.W.4 J."+y'-6y=0 y"+ 4y' + 4y = 0 y"+y=0 Subject to the initial conditions (0) = 2 and y'(0) = 1 y"- y = 0 Subject to the initial conditions y(0) = 2 and y'(0) = 1 y"+y'-12y = 0 Subject...
Solve the following system of equations. 2x+4y = 8 3x + 4y = 16 x = 0 Olo X y = -1
For the differential equation y" + 4y' + 13y = 0, a general solution is of the form y = e-2x(C1sin 3x + C2cos 3x), where C1 and C2 are arbitrary constants. Applying the initial conditions y(0) = 4 and y'(0) = 2, find the specific solution. y = _______
4. Solve the following initial value problems and sketch the solutions: (a) 4y" – 4y' + y = 0, y(1) = -4, y'(1) = 0 (b) y" + y' – 2y = 0, y(0) = 3, y(0) = -3 (c) y" – 2/2y' + 3y = 0, y(0) = -1, y(0) = V2