Solution
Given that
1 (a) For arbitrary real s find the exact solution of the initial value problem with...
Consider the initial value problem (a) Find the solution u(t) of this problem. u(t) = b) For t > O find the first time at which lu t = 10 A computer algebra system is recommended. Round your answer to four decimal places.) 回Show My Work (optional:@
Use mathematical induction to show that when n is an exact power of 2, the solution of the recurrence: { if n 2 2 T(n) for k> 1 if n 2 T(n) 2T(n/2) is T(n) n log
(1 point) Solve the initial value problem 10 10(+ 1) My – by = 241, 24t. for t> -1 with y(0) = 3. y=
Find the solution to the problem with the following initial
value:
We ask for an explicit solution. Justify each step of your
solution.
Indication:
where A and B are constants.
с22 dy 1 — 0, х > 0, у(0) — 1. у(1 + 2) х dx В и = A + 1 u 1u
Solve the y"+ 4y = initial value problem s 1 if 0<xsa To if x>,T ylo)= 1, g(0)=0
2. In each of the following find out if the subset S is a subspace of the vector space V. (a) V = R3, S = {x = (x1,T2, xs) : 2x1-3x2 +23 = 6). 一 山 (c) V = R2, S = {x = (xi, X2) : X1X2 > 0}
2) (a)(10 pts.) Find the continuous solution to the initial value problem de + y = 9(2) where q() = { 0 if 2>1 sat S 1 if |2<1. satisfying y(0) = 0. (b)(10 pts.)Solve the differential equation de ty
Let u be the solution to the initial boundary value problem for the Heat Equation, фа(t, x)-5 &n(t, x), t E (0,00), x E (0, 1); with initial condition 2 r-, 1 and with boundary condition:s n(t, 0)=0, rn(t, 1-0. Find the solution u using the expansion with the normalization conditions vn (0)-1, wn a. (3/10) Find the functions wz, with indexn> 1 b. (3/10) Find the functions v, with index n> 1. c. (4/10) Find the coefficients cn, with...
Solve the initial value problem ry' + xy = 1, > 0 y(1) = 2.
l. Let wn > 0 and 〈 > 0. Show that s2 + 2(Wns+uậ = 0 has (a) complex roots when 0 < £1. (b) real and equal roots when ς-1, and real and distinct roots when ς > 1