Problem 3. Solve the following systems of ODE's. ) -2 and 2(0)- 0. subject to the conditions y(0)...
3. Solve the following LTI ODE's using the Laplace transformation (a) +3y 0, y(0) 1, y(0) 2 (b) 3y sin(t), y(0) 0, (0 0 (c) 3y sin(t), y(0) 1, (0) 2 y-Sin(t),
please solve #2 Solve the following problems subject to the given boundary conditions. Show the formulas for any arbitrary constants (Ao, An, Bn), but you do not need to actually calculate them tu a(0. t)=0. u(1, t) = 5 u(z,0-82-1 2 0< x<2, t0 u(0, t) = 0, u(2. t) = 0 a(x, 0) 0, tr(r,0) = 0 3 ー+-=-10, 0
Question 3: BVP with periodic boundary conditions. Part I: Solve the following boundary value problem (BVP) where y(x,t) is defined for 0<x<. You must show all of your work (be sure to explore all possible eigenvalues). агу д?у 4 axat2 Subject to conditions: = y(x,0) = 4 sin 6x ayi at = 0 y(0) = 0 y(T) = 0 Solution: y(x, t) = Do your work on the next page. Part II: Follow up questions. You may answer these questions...
Problem 3 Solve the unsteady heat conduction problem: subject to the boundary conditions: u(0,t)0, (1,t)1; and the initial condition ua, 0) and sketch the form of the complete solution.
Solve the following systems subject to the given initial conditions. Comment on the nature of the singular point. (a) r +5y 1 (0)=1, y (0)=-1 0 44 -1 1 4 X (0)1 Solve the following systems subject to the given initial conditions. Comment on the nature of the singular point. (a) r +5y 1 (0)=1, y (0)=-1 0 44 -1 1 4 X (0)1
Solve the following ODE's for Y(x) A) x2y''-2xy'+2y=0 y(1)=2 y'(1)=1
Solve the following ODE's for Y(x) A) x2y''-2xy'+2y=0 y(1)=2 y'(1)=1
Consider the problem minimize 1[r(-)] = 2 / r,(t)2 dt subject to the conditions r(0) - r(T)0 and the constraint 0 r(t)2 dt 1. = Suppose that r : [0, π] R is a C2 function that! solves the above Let y : [0, π] R be any other C2 function such that y(0) Define problem a(s): (r(t) + sy(t))2 dt and a(s) a. Explain why a(0) 1 and i'(0) 0. b. Show that i'(0)= | z'(t) y' (t) dt-X...
Peoblem 3: Solve the following problems Problem 3. Solve the following problems: (a) y+ ty -y-0, y(0)-0, (0) 1. (b) ty"+(1 -2t)-2y0, y(0) 1, y'(0) -2 (c) ty" + (t-1)/-y 0, y(0) 5, lime y(t) 0. t-+00 Problem 3. Solve the following problems: (a) y+ ty -y-0, y(0)-0, (0) 1. (b) ty"+(1 -2t)-2y0, y(0) 1, y'(0) -2 (c) ty" + (t-1)/-y 0, y(0) 5, lime y(t) 0. t-+00