The dynamic model for a process is given by d2y/dt2+6dy/dt+8y=3u(t) where u(t) is the input function and y(0) and dy/dt(0) are both zero.What are the functions of the time (e.g.,e−t/τ) in the solutionfor each of the following cases?(a)u(t)=be−2t (b) u(t)=ct b and c are constants.Note:You do not have to find y(t) in these cases. Just determine the functions of time that will appear in y(t).

Q: uppose a 32-pound weight stretches a spring 2 feet. If the weight is released from rest at the…

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Q: 2. Ifƒ (x, y) = log (x² + y²), then ƒ +ƒ is equal to XX yy 1 (a) x² + y² (b) 0 1,² - x² (c) (d) *…

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Q: Find the linearization of the function f (x) = x' at x = 1. L (x) =

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Q: Q2: If D = d dt > find a complete solution of: (D+2)x+ (D+4)y = 1 (D+1)x+ (D+5)y = 2

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Q: a) Show that y=e*is a solution of the linear D.E y'+y=0, and y =xis a solution of the nonlinear D.E…

A: Please find solution of both parts.

Q: The values of C, and C₂ so that y(x) = C₁x + C₂ (-) satisfies the two conditions y(1) = 1 and y'(1)…

A: Given: yx=C1x+C2-13x2 To find the values of C1 and C2 such that y1=1 and y'1=-1.

Q: Find the linear approximation to f(x)=x2+1x−2 near a=3.

A: Given: f(x) = x2 +1x − 2; a = 3

Q: Suppose a 32-pound weight stretches a spring 2 feet. If the weight is released from rest at the…

A: In this question, we set up the differential equation for the given data and then solve by using…

Q: Solve the simultaneous ODES (a) x"(t) + 4x(t) + 5y(t) = t²,_y"(t) + 5x(t) + 4y(t) = t +1

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Q: 2. Identify the iterative function f(x) = x3 – 9x2 – 6 if initial approximation x, = 2.25

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Q: Find x and y for which the following equation is satisfied: x+2 = - 5+i i-5

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Q: If f(x) = S5 (t³ + 7t² + 3) dt then f"(2) =O

A: To find the second order derivative , we first invoke the fundamental theorem of calculus , which…

Q: Suppose that an insect population, r(t), is controlled by a natural predator population, y(t). (a)…

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Q: = (15) Determine whether or not the functions y₁ 4x³, y2 = π, y3 = 12x², and y4 = 24x are linearly…

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Q: f(x)= k(3x + 4), x = – 1,0,1,2 Find second moment E(X').

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Q: With the understanding that D = , find a complete solution of the dt following: (D + 5)x + (D + 3)y…

A: Given: D+5x+D+3y=e-t      ....(1)and   D+2x+D+1y=3        ....(2)On solving (1) and (2) we…

Q: The function y =x is one the solution of (x-1)y-xy'+y= 0. we use reduction to order method, second…

A: Given y=x is one solution of x-1y''-xy'+y=0. Let, y=vx be another solution of the given equation.…

Q: Show that a linear equation dy a(x)- + b(x)y = c(x) d.x %3D is exact if a' (x) = b(x).

A: Given linear differential equation axdydx+bxy=cx.....1 We have to show that the given differential…

Q: show that the solution y(t)=e^2tsin(t) is linearly independant.

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Q: 3. Given the following graph and A(x)= [f(t) dt, find: A(4)= 4 y=f(t) 3 A(6) = 1- A(10)= A'(x)= -2

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Q: Į va | Vi(t? + 6t +7) dt. 4. Find

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Q: Find y as a function of a if y(0) = 5, y(0) = 17, y"(0) = 5, y"(0) = 8. y(x) = y(4) — 6y" + 9y" =…

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Q: x A(x) = † (3-1²) dt 0

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Q: Solve the IVP dx dt [ x(t) = 12 0 X, -24 0 x(0) = [13] 181

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Q: If F(x)= -3 f (t)dt and f(17) = 4; find F'(7) 2x=3

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Q: d/dt ŷ = [3 1] ŷ, ý(0) = [8] [-2 1] | [6]

A: Given that dy^dt=31-21y^ with initial condition y^(0)=86 Let A=31-21 and eigenvalue of A is λ. Then…

Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear…

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Q: The Lotka-Volterra equations are often used to model the links between a particular population of…

A: (a) f(u, v) at u = 0.6 and v = 50 f0.6, 50 = -0.5×0.6+0.6×50100 = 0 f(0.6, 50) = 0

Q: 5) State any theorems that you use in determining your solution. a) By using partial differentiation…

A: a) Suppose we have n pairs of values yt, xt t=1,2,...,n  yt=α+βxt+ut where  yt=Dependent…

Q: If R(t) = (3t 2 -t) i + (2- 6t) j - 4t k , find (a) R(t) dt and (b) R(t) dt.

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Q: Determine three linearly independent solutions to the equation y" + 2y" – 3y = 0 of the form y(x) =…

A: The given differential equation is                                                y'''+2y''-3y'=0

Q: V3 (9) 1 x' x(0) = V3 - 1

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Q: Find the general solution of the fourth order linear equation y(4) + 4y" + 4y = 0.

A: Given problem is :

Q: Q2. (a) If b – 4ac = 0 and y1 = emz solves ay" + by' + cy = 0, use reduction of order to get a…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.