(*) Find the cigenvalues and eigenfunctions for the following problem: - = A, 0 < x...
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
Problem 2: [Also challenging] Find the solution of the following IVP: y' +2y = g(t), with y(0) = 3 where g(t) = - 0<t<1: g(t) = te-2 > 1.
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.
Solve the y"+ 4y = initial value problem s 1 if 0<xsa To if x>,T ylo)= 1, g(0)=0
(2) The circuit is at steady state for t<0. Find v(t) for t>0. Answer t=0 ZF Navt)14 T
Problem Three (1) Write the expression that defines the expectation value of the operator <x> for any function Y. (II) Find the expectation value of <x> for the particle in a box defined by the wave function: Y=N(L x - X°) within limits ( < x < L. which you previously normalized in Problem Two on the previous page.
(1 point) Consider the following initial value problem: y" + 36y= 0 <t< 5 t> 5 y(0) = 4, y'(0) = 0 Using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s) =
7. Find the solution of the heat conduction problem 100uzz = ut, 0 < x < 1, t > 0; u(0,t) 0, u1,t 0, t>0; In Problem 10, consider the conduction of heat in a rod 40 cm in length whose ends are maintained at 0°C for all t0. Find an expression for the temperature u(,t) if the initial temperature distribution in the rod is the given function. Suppose that a
Please help me solve this differential Equation
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Find a continuous solution satisfying +y-f(x), where f() Ji 10 { 0<r<1 > 1 and y(0) -0.
How to solve it?
Let F =< -2, x, y2 >. Find S Ss curlF.nds, where S is the paraboloid z = x2 + y?, OSz54.