Just b and d 3. Solve the initial value problems. a) z' + (5/t)x = 1...
3. Use Laplace transforms to solve the following initial value problems. Write the solution (t) for t20 as a simplified piecewise defined function. (a) z', + 2x' + 2x-f(t), x(0-0, z'(0)-i, where f(t)-〈0 otherwise. (b) z', +x-f(t), x(0) 0, z'(0)=1, where t/2 if 0 t< 6, 3 ift26 f(t) 3. Use Laplace transforms to solve the following initial value problems. Write the solution (t) for t20 as a simplified piecewise defined function. (a) z', + 2x' + 2x-f(t), x(0-0, z'(0)-i,...
question 1,2,3 please Special Functions- IVP and BVP Quiz 3.12 Solve the following initial value problems. Ans: y- cost+ H(-3)-cos(t 2r) H(t3) y(0)=0,s(0)=1 where 2. v', +y=g(t), { 1, 0 t<π/2 g(t) = Ans:y=1-cos t + sin t + (sint-1)H(t-π/2) x(0) = 0,d(0) = 1 where 3、z"(t) + 162(t) = g(t), cos 4t, 0 12π. t<π 5 Special Functions- IVP and BVP Quiz 3.12 Solve the following initial value problems. Ans: y- cost+ H(-3)-cos(t 2r) H(t3) y(0)=0,s(0)=1 where 2. v',...
Problem 1: Solve the initial value Dirichlet problem on the half-line and find the value u(1, 2): (8 points) tut(t, z) - trọt, c) = c+t, (t, x) R x [0, +x), u(0, 2) = cos(V), 4(0,2)=e", u(t,0) = 1+ t.
Use the Laplace transform to solve initial value problems 3. tx" + 2(t-1)x' - 2x = 2, x(0) = 0.
PDEs...Just 1 and 2 Problem 1: By writing nm1 where (An are the associated eigenpairs, solve e kus +9(x, t) with k = 1, g(z, t)-cos x, u,0,t)-ur(2nd) = 0, u(z,0) = cos r + cos 21. 2. 3. k = 1, g(z, t)--_exp_2t)sinz, u(0,t) = u(z,t) = 0, u(z,0) = sinz. Problem 1: By writing nm1 where (An are the associated eigenpairs, solve e kus +9(x, t) with k = 1, g(z, t)-cos x, u,0,t)-ur(2nd) = 0, u(z,0) =...
Use the Laplace transform to solve initial value problems 5. *" + 4x = f(x); x(t) = 35. f(t – 1) sin 27 dt, x(0) = x'(0) = 0 (use a convolution theorem).
Let u be the solution to the initial boundary value problem for the Heat Equation, au(t,z 382u(t,z), tE (0,oo), E (0,3); with initial condition u(0,x)-f(x)- and with boundary conditions Find the solution u using the expansion u(t,x) n (t) wn(x), with the normalization conditions vn (0)1, Wn (2n -1) a. (3/10) Find the functionswn with index n 1. b. (3/10) Find the functions vn, with index n 1 C. (4/10) Find the coefficients cn , with index n 1. Let...
3. (20pts) You are given that .. (5+ X +2) +1 +2 Solve the initial value problem using the method of Laplace transforms. y+u(t)e-*, y(0) =1
1. Solve the boundary value problem ut =-3uzzzz + 5uzz, u(z, 0) = r(z) (-00 < z < oo, t > 0), using direct and inverse Fourier transforms U(w,t)-홅启u(z, t) ei r dr, u(z,t)-二U( ,t) e ur d . You need to explain where you use linearity of Fourier transform and how you transform derivatives in z and in t 2. Find the Fourier transform F() of the following function f(x) and determine whether F() is a continuous function (a)...
advanced math homework help before final 5. Consider the following initial value problems: x" + 16x = -20e-2 x(0) = 1 2'0) = 0 (a) (4 points) Solve for X(s), the Laplace transform of r(t). (b) (10 points) Solve for e(t) by inverting X(s). (c) (3 points) Let yt) = 2 cos(4t) - 7 sin(4t) (This is one of the pieces to your answer above). Fill in the right-hand sides to the initial value problem that y solves y (0)...