Solve the initial value problem (IVP) Ut + 3ux + 3u 0, u(x,0) = x2, (x,...
5. (20 pts). Solve the following initial-value problem: Ut + 2uuz - 0<x<, 0 <t<oo 0 1 <1 > 1 u(t,0) = Then draw the solution for different values of time.
Consider the initial value problem 3u" - u'+ 2u = 0, u(0) = 5, u'(0) = 0. (a) Find the solution u(t) of this problem. u(t) = _______ (b) For t > 0, find the first time at which |u(t)|=10. (A computer algebra system is recommended. Round your answer to four decimat places.)t = _______
Problem 1: Solve the initial value / Dirichlet problem on the half-line and find the value u(1, 2): (8 points) Utt(t, 2) – Uzz(t, x) = x+t, (t, x) ER [0, +co), u(0,x) = = cos(2), ut(0, 2) = e", u(t,0) = 1+t.
(1) Solve the initial Value Problem (IVP): 2x+1 f'(x) = — ; f(0) = 1. x²+1 DE): frm=2* 31 (a) First, solve the differential equation (DE): f'(x) = 2x+1 — x2 + 1 1 2x+1 Hint: - x2+1 2 x 1 - + - x?+ 1 x2 + 1 2 x Guess a function whose derivative is x2 + 1x2+1 Gues humaian whose centraline a creative 1.a, tratan antarane element ;) 1 2 x 1 i.e., find an antiderivative of...
Problem 5: Consider the initial value Dirichlet problem ut(t, x) – 2uxx(t, x) = et, (t, x) € (0, +00)?, u(0,x) = 1, u(t,0) = e- For the unique solution u(x, t) find the following limit as a function of t: (8 points) lim u2, t). +00
Find a formula for the solution of the initial value problem for for t>0, -oc < x < oo ut = uzz-u a(1:0) = g(z) -x < 1 < x where g is continuous and bounded.( Hint: use v(x, t) = et u(z. t).)
Find a formula for the solution of the initial value problem for for t>0, -oc
Problem 5: Consider the initial value / Dirichlet problem ut(t, x) – 2uzz(t, x) = et, (t, x) € (0, +00)?, u(0, 2) = 1, u(t,0) = e- For the unique solution u(x, t) find the following limit as a function of t: (8 points) lim u(x, t). 2+
Solve initial value problem (IVP) dy 2y- х dx V x2 – 16 = 0, y(5) = 2
4. Solve the initial, boundary value problem by the Fourier integral method. u (0,t)0, u(r,t) bounded as-00
4. Solve the initial, boundary value problem by the Fourier integral method. u (0,t)0, u(r,t) bounded as-00
Solve the initial-boundary value problem for the following equation
U = N Ux with U(x, 0) = sin (x) +N ,U(0, t) = 0, and U, (N, t) = 0
Q4| (5 Marks)
my question
please answer
Solve the initial-boundary value problem for the
following equation U = N Ux with U(x, 0) = sin (x) +N ,U(0, t) = 0,
and U, (N, t) = 0 Q4| (5 Marks)
Solve the initial-boundary value problem for the following equation Uų...