Please show work. Choose the correct general solution of the with r(t) = { a, cos...
Show all work for credit General Solution Roots | y(z) = Genz + Cenz Two real roots r T2 One real root r Bi | y(z)-Geaz cos(ßz) + Ceaz sin(8z) Two complex roots a Form of p | Example f(t) | Example2 Form of f(t) A cos(t)+Bsin(at) 1. Find the general solution to the DE: y" +4y +4y Show all work for credit General Solution Roots | y(z) = Genz + Cenz Two real roots r T2 One real root...
Find the general solution of the equation y" + 361y = 0. y(t) = C1 cos 19t + c2 sin 19t o o o o y(t) = ci cos t-cı sin t y(t) = ci cos t+ c2 sin 19t y(t) = cı cos 19t+ c2 sin t
Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t 2x' + y' - 8x - 9y = e-t x' +y' +9x + 4y = et Eliminate y and solve the remaining differential equation for x. Choose the correct answer below. O A. X(t)= C1 e 7t + Cze - 7t + 58 e-t- et O B. X(t) = Cy cos (7t) + C2 sin (7t) OC. x()=C7 e...
Please show step-by-step solution and explain. Thanks! For each one of the following functions of t, indicate whether they are periodic or not. If periodic, indicate its period, and if not periodic, indicate why. Assume n is a positive integer. Sin (b) sin (xt) +cos (V3t) (c) sin ( 쭉 ) + cos (2nt) + sin ( 2F) + sin( (d) cos (2nt) (e) cos (xt) - cos (t) (f) sin (nt) cos (2nt) )
Please show solutions. Answer: 1. Find a general solution to the following differential equations: (a) y" + y = 0 (b) y" – 2y' + 264 = 0 (c) 4x²y" – 3y = 0 (d) y" + 4y = 9 sin(t). (e) y" – 6y' + 9y = 6e3x 1. (a) y = ci + c2e- (b) y = cle' cos(5t) + czet sin(5t) (c) y = cit-1/2 + c2t3/2 (d) y = ci cos(2t) + c2 sin(2t) + 3...
Solve the following questions and Choose the correct answer. 1) The General solution to y" + y = 0 sty -3&y(x) = -3 y = cos(3x) + sin(-31) , 3cos(x) – 3 sin(x) 3 ) 3 Answer 2) Suppose that y(t) and y(t) are two solutions of a certain second order linear differential equation, sin(t)y" + cos(t) y' - y = 0. 0<<< What is the general form of the Wronskian Wy ) (6) ? Without solving the equation. b)...
Use the method of variation of parameters to find the general solution y(t) to the given differential equation y" + 25y = sec (5t) Oy(t) = ci cos(5t) + c2 sin(5t) tan(5t) + 25 sec(26) 25 y(t) = c cos(5t) + c sin(5t) 1 sec(56) + 50 1 25 tan(5t) sin(5t) VC) = so 1 sec(5t) + 50 1 tan(5t) sin(5t) 25 1 y(t) = ci cos(5t) + c) sin(5t) 2. sec(54) + tan(56) sin(56) 50 O y(t) = C1...
Please show all work with clear handwriting a) Compute the Wrornskian of the set {e* cos 3x, ex sin 3x} b. Show that {ex cos 3x, ex sin 3x} form a fundamental solution set for y" – 2y' +10y = 0 on the interval (-00,00) and write the general solution
The general solution y(t, p. 6) to the wave equation on a disc of radius R with boundary condition v(t, R, 1) = 0 is given by vlt,0,0) = EE - ( ) [cos (ES) (Am.cos(nb) + Bu sin(no)) + (ME) (C..cos(no) + Dm (no) n=0 s=0 sin sin(ne)) 728 where Jn (2) is a Bessel function and x is the s'th root of In(x). (i) Derive the expressions for y and Oy/at at t = 0. (ii) Find all...
You are given that yh = c1 cos(3x) +c2 sin(3x) is the general solution to the homogeneous differential equation y 00 + 9y = 0 (a) In each case below, write down your “guess” for the form of the particular solution to the differential equation. y 00 + 9y = f(x) Question 6. (Total marks: 14) You are given that y = cos(3x) + sin(3.c) is the general solution to the homogeneous differential equation y" +9y = 0 (a) In...