The general solution y(t, p. 6) to the wave equation on a disc of radius R...
Match each given vector equation with the corresponding curve. y4 0 b a (0, 1,0) (1,0,0 , 1,0 d C 2 A (0,0. 2 y- r(t)= (, ? r(t) (sin (t),t) r (t) (t, cos (2t), sin (2t)) ? v r (t) (1 +t,3t,-t) r (t) (t)i-cos (t)j+sin (t) k =COS r(t)=i+tj+k r(t) i+tj+2k r(t)= (1,cos (t).2sin (t) Match each given vector equation with the corresponding curve. y4 0 b a (0, 1,0) (1,0,0 , 1,0 d C 2 A...
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
<---- equation (6) Using the equation (6) in page 569 of our text, obtain the solution of ut-CUx -lx in integral form satisfying the initial condition u(x, 0) = e- 30 1 | [A(p) cos px + B(p)sin px) e-c2p2tdp 11 (x, t; p) dp= u(x, t)= 0 Using the equation (6) in page 569 of our text, obtain the solution of ut-CUx -lx in integral form satisfying the initial condition u(x, 0) = e- 30 1 | [A(p) cos...
1.- The given family of solutions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial value problem (a) y = cie" + c2e-, 2€ (-0,00) y" - y = 0, y(0) = 0, 10) = 1 y=cles + cze-, 1€ (-00,00) y" – 3y – 4y = 0, y(0) = 1, y(0) = 2 Cl2 + 2x log(x), t (0, x) ry" – ry'...
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...
Please show all work and answer all parts of the question. Show that the solution to the following 1-D wave equation on a semi-infinite domain = 36 , y(0, t) = 0, t2 0, y(, 0 (r,0) 0 in(2 cos(w is given by y(x,t) =- r) cos(6w t) d Show that the solution to the following 1-D wave equation on a semi-infinite domain = 36 , y(0, t) = 0, t2 0, y(, 0 (r,0) 0 in(2 cos(w is given...
4. Applications of Laplace transform Questions 1-4, find y(t) (1). y(t)=t+ſ v(7) sin(t – r)dt (2). y(t)=1-1 "(t)edt (3). y'(t)=t+ſ v(t = 1)cos edt , y(0)=0 (4). y'(t)=1-1 y(t-1) edt, y(0)=1
Let y: 1 + R2 be a regular parametrised curve which we write as y(t) = (v(t), v(t))" for some smooth maps u,v: 1 R. We assume furthermore that is never equal to zero on I. We define the surface of revolution Exy associated to y as (1) E = {r(t,0) = (v(t) cos(6), y(t) sin(0), v(0))?|tel, 0 € (0,27]} . Below, we consider the chart (U,r) obtained by taking U = I x (0,27), where the map r:U →...
Question 2 2 p The differential equation whose general solution is Y=C1 Cos( V7x)+C2 Sin (7x) O y +6y'=0 O y"- 7y=0 O y +7y=0 Activate W Go to Sets
5. A return to the circular disc problem examined in class (Lecture 2): (Despite all of the text below you are required to do very little. Please read on.) A thin, circular plate assumed to lie on the ry-plane is rotating about its center O, located at (0, 0), with constant angular speed w. (w > 0 means that the plate is rotating in the counterclockwise direction.) Using the results obtained in class, show that the velocity field of of...