5. Find the largest interval a <t<b such that a unique solution of the given initial...
For the following linear, second-order IVP, find the largest interval on which a unique solution is guaranteed to exist. +2-1 y" + +12y + cos(t) (t+2) sin(t) Y = y(2) = 11, y(2) = 4 t+1)
4. Write the initial value problem in matrix form X' = AX + f(t), X (to) =< b1,b2, 63 > and then find the largest interval centered at to =0 where the initial value problem will have an unique solution. '(t) = 3x + 2y - 2+t?, (to) = 3 yt) 2-2y - z+ vt +4, y(to) = 3 z't) 3x + 2y - 2+3, z(to) = 3
Find the solution of the given initial value problem: y" + y = f(t); y(0) = 6, y'(0) = 3 where f(t) = 1, 0<t<3 0, įst<<
4. [10] Find the solution to given initial-boundary value problem: 4uxx = ut 0<x<TI, t> 0 u(0,t) = 5, uit, t) = 10, t> 0 u(x,0) = sin 3x - sin 5x, 0<x<T
4.[10] Find the solution to given initial-boundary value problem: 4uxx = U, 0 < x <TT, t> 0 u(0,t) = 5, u(t, t) = 10, t> 0 u(x,0) = = sin 3x - sin 5x, 0<x<
6.[10] Find the solution to the vibrating string problem governed by the given initial-boundary value problem: 9uxx = Utt 0<x< 1, t> 0 u(0,t) = 0) = u(tt,t), t> 0 u(x,0) = sin 4x + 7 sin 5x, 0<x< 1 uz (3,0) = { X, 0 < x < 1/2 r/2 < x <
Find a general solution to the given equation for t<0. y''(t) – Ły'(t) + 5 -y(t) = 0 t The general solution is y(t) = (Use parentheses to clearly denote the argument of each function.)
Find all integers x, y, 0 < x, y < n, that satisfy each of the following pairs of congruences. If no solutions exist, explain why. (a) x + 5y = 3(mod n), and 4x + y = 1(mod n), for n = 8. (b) 7x + 2y = 3(mod n), and 9x + 4y = 6(mod n), for n=5.
Find the Laplace transform Y (8) = L {y} of the solution of the given initial value problem. St, 0<t<1 y" + 4y = {i;isica , y0 = 8, Y' (0) = 6 Enclose numerators and denominators in parentheses. For example, (a - b)/(1+n). Y (3) = QE
Determine the largest interval (a,b) for which Theorem 1 guarantees the existence of a unique solution on (a,b) to the initial value problem below. **x + 3y" - 2xy +y=0y(-)=1.0 (-5) =0.5" (-6) -- o or in interval notation.) (Type your answer in interval notation.)