da(t) ? Assume theWhich of the following is a fundamental set for a system defined by differential equation d*y()dt+ 4y (t)dtdtinput x (t)-2tu(t) and with conditions y (0) = 0;= e= 1O C1 e3tO C, etO 4 et

The given differential equation is d2y(t)dt2+5dy(t)dt+4y(t)=dx(t)dt. The given input equation is…

Answered: dæ(t) ? Assume the Which of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Match the direction field with systems of differential equation
U = U(x,y,z, t) = [sin(kx) + cos[ny] + sin(mz)]e-100t Calculate the numerical values of the constants k, n and m so that the function can be the solution of the partial differential equation given below. a²U + dx2 a²U 1 aU ду? 16 dt
Activity 3: The car body vertical displacement, y(t), can be approximately modelled as a damped mass-spring system (called car suspension system) using the following differential equation: Car Body Attaches Here Spring and Damper Hub Assembly ННИНЯТ d²y + b₂ dt² Wheel and Tire dy dt + ky = f(t) k Car body mcar 4 bv y (t) f(t) 7/1 Where y(t) is the vertical displacement, mear is the car mas, b, is the damping coefficient, k is the spring stiffness constant, t is the time, and f(t) is the hight of the street from the ground level as a function of time. Given that m = 1500 (Kg), b₂ = 2000 (N.s/m), and k = 100000 (N/m). Answer the following questions: (3-A) If the street is straight, so the f(t) = 0, determine the general solution of y(t). (3-B) Given the initial conditions y(0) = 2, and y'(0) = 1, determine the particular solution of y(t). (3-C) Use Laplace transform to solve the given differential equation with the same initial conditions given in (3-B).
Consider the differential equation (D₁) : 2x(t) — 8e¯ï(t) + 5 = 0, x(0) = ln(4) and the relation y(t) = e(t) — 3. 1. Show that y(t) satisfies the differential equation (D₂): 2y(t)+5y(t)+7= 0, y(0) = 1 if and only if x(t) satisfies the differential equation (D₁). 2. Find the backward solution of (D₂) and deduce the backward solution of (D₁). 3. Is the solution of (D₁) convergent or divergent? Justify your answer.
can you please provide explanations
As above, let Suppose Compute ||B||2 to the nearest hundredth. Answer: 8 9 -3 A = 40 9 -6 5 1 -1 10 B = A (49) A
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Pls answer a b c and d.
Match the direction fields labeled A through D with the differential equation below. A B D 1. y = zy + y 2. y' = y+ 3z 3. y' = y - 3r 4. y = 2 - zy
q13
The first-order linear differential equation written in the form M dx + N dy = 0 has an integrating factor of: A u=e. u=e u=e D
4. Rewrite the given differential equation as a system of first order differential equations: - 2+2y=e²t Sint, 0 < t <1, y(0) = -0.4 and y'(0) = -0.6 d²y dt² 5. Given: d²y dy 2 + 2y = e²t Sin t, 0

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dæ(t) ? Assume the Which of the following is a fundamental set for a system defined by differential equation d de + 4y (t) dt dt input x (t) -2"u(t) and with conditions y (0) dy = 0; = 1 = e O C1 e3t O C4 et O q et O q e st