4. Which of the following is a solution to the PDE i (a) (a) ucos cr...
just need the answer please
Question 3 Give the general solution to r'y'+ 2 y -2 cos(3z) y 1/2 3/2 r3 sin(3r) +Cr a) b) y/2 sin (3z) + Cr 3 = T 3 sin(3z) + Cr c) y 3/2 sin(3z) + Cr 3 d)y1/2 1/2 r sin (3r) + Cr e) None of the above. Question 4
a) Find the solution to the following interior Dirichlet problem with radius R=1 1 PDE Urr + Up t 0 0 <r <1 wee p2 r BC u (1,0) = 10 + 3 sin(0) 10 cos(20) 0 <0 < 27 b) Consider the above problem on the unit square (x,y) domain PDE Urr + Uyy = 0 0<x<1 0<y <1 Transform the solution u(r, 0) from "a)" to the solution u(x, y) for "b)" Use the solution u(x,y) to calculate...
Consider the following second order PDE Uit – 9Uxx = 0, 0<x< < t > 0, (A) and the following boundary value/initial conditions: Ux(t,0) = uſt, 5) = 0, t>0, u(0, x) = 44(0, x) = 4 cos’ x, 0<x< (BC) (IC) for the function u= u(t, x). a. (5 points) Find ordinary differential equations for functions T = T(t) and X = X(x) such that the function u(t, x) = T(t)X(x) satisfies the PDE (A). b. (5 points) Find...
Question 11 Give the form of a particular solution of (4) – 16y-2 e 2x+3e" + cos2x) – 1 a) z-Axe* + Be **+Ccos(2x) + sin(2x) + E d) Axe 2+Be+Cx cos(2x) +Dx sin(2x) +B 3-Axe* +Be+3+ Cx cos(2x) +Dx sin(2x) + E 2=Axe 2+36-3x+cos(2x) + sin(2x) -Ae 2*+Be9*+ C'x cos(2x) + DX sin(2x) + E None of the above. e) f) Question 12 Give the form of a particular solution of J14) - 4 7 " +13 y" –...
Problem # 1 [15 Points] Consider the following PDE which describes a typical heat-flow problem PDE: ut = ↵2uxx, 0 < x < 1, 0 < t < 1 BCs: ux(0, t)=0 ux(1, t)=0 0 < t < 1 IC: u(x, 0) = sin(⇡x), 0 x 1 (a) What is your physical interpretation of the above problem? (b) Can you draw rough sketches of the solution for various values of time? (c) What about the steady-state temperature?
-1-1 arctan n n" n!5* (c) Find the interval of convergence and radius of convergence for )0301 i )e-3r) (d) Use the geometric series to write the power series expansion for i. f(1)- 2-4r, centered at a = 0. i.)4 centered at a-6. (e) Write the first 4 nonzero terms of the Maclaurin expansion for i, f(z) = z2 (e4-1) ii. /(x) = cos(3r)-2 sin(2x). (0) Use the Taylor Series definition to write the expansion for f(a)entered at (8) Use...
Problem 2 Consider the one dimensional version of the heat PDE in Problem1 2 0x2 a(0, z) = uo(z) = e-r2. (a) Write down the Fourier transformed version of (2). Then, find the solution of this transformed version u(t,)-((,) (b) Invert the solution in part (a) to get the solution, u(t, x)-F-(u)(t, x), to (2)
Problem 2 Consider the one dimensional version of the heat PDE in Problem1 2 0x2 a(0, z) = uo(z) = e-r2. (a) Write down the...
Question 21 (3 points) Saved day Which of the following is a solution to the wave equation, aly dt2 Oy = e-* sin (kx – wt) Oy = (cos kx) (sin t) Oy = e-* sin at y = esin x Oy = e-* cost Actually, all of these are solutions to the wave equation. Actually, none of the above is a solution to the wave equation.
- A vector tangent to the parametric curve given by r (t) = <cos (4t); sin (4t); e^(t^2)> at the point (0; 1; e^((pi/8)^2)) is a) (0; 1; e^((pi/8)^2)) b) (0; 4; e^((pi/8)^2)) c) (4; 0; e^((pi/8)^2)) d) (4; 4; e^((pi/8)^2)) e) None of the above - The curve c (t) = (cost, sint ,t) lies on which of the following surfaces: (a) cone (b) cylinder (c) sphere (d) plane (e) none of the above
4. The solution of the inequality x2 – 4 < 0 is (a) –2 < x or x > 2 (b) –2 < x < 2 (C) x>-2 (d) x < 2 (e) None of the above 5. The domain of the function f(x) = V2is (a) (-2,2) (b) (-0, -2) U (2,00) (c) (-0, -2] U (2,0) (d) (-20, -2] U (2,00) (e) None of the above 6. The range of the function f(x) = 2 sin(x) is (a)...