The differential equation ay" + by' + cy = f(t) has characteristic equation aλ2 + bλ...

The differential equation ay" + by' + cy = f(t) has characteristic equation aλ2 + bλ + c = 0 whose roots are given in each part below. The forcing function f(t) is also indicated. Sketch the form of the homogeneous solution to the differential equation. Indicate the algebraic form of a particular solution. Sketch the form of the general solution for y(0) = y' (0) = 1.

(a) λ = −2, −3, f(t) = e −2t

(b) λ = −3, −3 (repeated real root), f(t) = sin(3t)

(c) λ = ±3i, f(t) = sin(2t)

(d) λ = ±3i, f(t) = sin(3t)

(e) λ = −2 ± 3i, f(t) = sin(3t)

Expert Solution

Colby Messinger answered 1 year ago

Solve the differential equation Y’(t) = AY(t), with initial condition Y(0) = [1;0] (a 2x1 matrix);...

Solve the differential equation Y’(t) = AY(t), with initial condition Y(0) = [1;0] (a 2x1 matrix); where A = [ 9 , 5 ; -6 , -2 ]. Then, using Euler’s method with step size h=.1 over [ 0 , .5 ] fill in the table with header where the 2x1 matrix Yi is the approximation of the exact solution Y(ti) : t Yi Y(ti) ||Y(ti) – Yi ||

D^2 (D + 1)y(t)= (D^2 +2)f(t) a.) Find the characteristic polynomial, characteristic equation, characteristic roots, and...

D^2 (D + 1)y(t)= (D^2 +2)f(t) a.) Find the characteristic polynomial, characteristic equation, characteristic roots, and characteristic modes of the system. b.) Find y_o(t), the zero-input component of response y(t) for t>=0, if the the initial conditions are y_0 (0) = 4, y_0' (0) = 3, and y_0'' (0) = -1

(a) What is the Black-Scholes Partial Differential Equation for the price f(t,St) at time t of...

(a) What is the Black-Scholes Partial Differential Equation for the price f(t,St) at time t of a European derivative security on a stock with price St? Specify the meaning of the terms or symbols in the equation. (b) Note that the Black-Scholes Partial Differential Equation does not specify whether the derivative is a call option, a put option, or some other derivative. How do you incorporate the derivative payoff when using Black-Scholes PDE to price a derivative?

Ax = 6m and Ay= -8m, Bx= -8m and By= 3m, Cx = 27m and Cy=...

Ax = 6m and Ay= -8m, Bx= -8m and By= 3m, Cx = 27m and Cy= 21m. Determine a and b such that aA + bB + C = 0. Include a sketch of the scenario.

Solve the differential equation. x''(t)+2x'(t)+5x(t) = 2

Plot the solution of the equation 6ẏ + y = f(t) if f (t) = 0 for t + 0 and f(t) = 15 f

Plot the solution of the equation6ẏ + y = f(t) if f (t) = 0 for t + 0 and f(t) = 15 for t ≥ 0. The initial condition is y(0) = 7.

Show that the set of all solutions to the differential equation f′′+f=0, where f∈F(R), is a...

Show that the set of all solutions to the differential equation f′′+f=0, where f∈F(R), is a real vector space with respect to the usual definition of vector addition and scalar multiplication of functions

Find general solution to the differential equation x'(t) = Ax(t) + v, A = [ 2...

Find general solution to the differential equation x'(t) = Ax(t) + v, A = [ 2 −2; 2 2] , v = (2 0) .

Let y(t) = (1 + t)^2 solution of the differential equation y´´ (t) + p (t) y´...

Let y(t) = (1 + t)^2 solution of the differential equation y´´ (t) + p (t) y´ (t) + q (t) y (t) = 0 (*) If the Wronskian of two solutions of (*) equals three. (a) ffind p(t) and q(t) (b) Solve y´´ (t) + p (t) y´ (t) + q (t) y (t) = 1 + t

Applied Math Let T be the operator on P2 defined by the equation T(f)=f+(1+x)f' (a) Show...

Applied Math Let T be the operator on P2 defined by the equation T(f)=f+(1+x)f' (a) Show T i linear operator from P2 into P2! (b) Give matrix reppressentaion in base vectorss B={1,x,x2}! (c) Give a diagonal matrix representing T (d) Give a diagonal matrix representing T Where P2 is ppolynomials with degree less then or equal to 2 and f' is the derivative of polynomial f.

Question