2. Find the DE of the system below, given that r(t) = t²e¬tu(t), where u(t) is a stepfunction. s2 -s+1 C(s) R(s) s5+3s4 +2s² +1

Q: Q3: find x, y and z for the following system by using Gramer's rule? 1 - 3 x - 2 z 2 z + y = 0 1 2 y…

A:

Q: Consider the system: x + -1 y = (1 0)x Suppose the input is µ(t) = e-t and that the output is y(t) =…

A:

Q: الإنجليزية Q3: It is required to find the general solution of the following system dx =y+z dt (1) dy…

A: Second-order linear equations with constant coefficients. The generic form of an equation like this…

Q: Determine the values of the parameter s for which the system has a unique solution, and de Sx1 -…

A:

Q: For the O a. O b. OC. time-invariant system x' = Ax for which Ø(t) = eAt where: d. Ø(t) = [0(t)]-¹…

A: Solution :-

Q: A D 15. Classify the system of equations. Sy = 5z – 1 ly = 6z +2 Consistent and Dependent…

A: Given:  y=5x-1y=6x+2 To find: Classify the system of equation.

Q: Apply the method of undetermined coefficients to find the particular solution to the following…

A: Given x'=6x+18y+1, y'=2x+6y+3, x0=3, y0=-3

Q: For which value of a the system of ODES Ý1 = ayı + y2+ (e¯½ – 1), j2 = -Y1 + 2ay2 has stable node at…

A:

Q: The table below shows the projected values (in millions of dollars) of hardback college textbooks…

A: Consider the provided question, The table below shows the projected values (in millions of dollars)…

Q: What are the roots of the characteristic equation of the following system? d.x 22+2y-3z dt dy…

A: First write the system of differential equations in the matrix form. Then use the formula,…

Q: 1. Find y by Cramer's rule for the following linear system. I+Oy+22 6 -3r+4y +62 30 -r-2y+3z=S

A: “Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: The table below shows the projected values (in millions of dollars) of hardback college textbooks…

A: We will find out the required values.

Q: Q2. Consider the system below y[n] xa(t) C/D H(@) T Where T = 0.001s and |w] < 0.57 to otherwise…

A: output of C/D block will be:

Q: Solve y" + y = F(t), in which F(t) = 1– t²/n² if 0 <t<n and F(t) = 0 if n<t; here, y(0) = 0, y'(0) =…

A: To find- Solve y'' + y = Ft, in which Ft = 1 - t2π2 if 0 ≤ t ≤ π and Ft = 0 if π &lt; t; here y0 =…

Q: For which value of a the system of ODES —D У1 + ау2 + (е -У — 1), У2 3D —ауј — У2 has an unstable…

A:

Q: Q2:B. Consider a continuous-time system with the input-output relation: y(t) = T{x(t)} = x(1)8(1 –…

A:

Q: What is the general solution for the system x (t) = x1+ 2æ2, a', (t) = 2x1 + x2? O7 = c1[1,1]e 3*t +…

A: option third is correct  see below the calculation

Q: 2. Determine the expressions for the unit step response for the systems represented by the following…

A: 2) ii  Given,X0sxis=10s2+65+5Given , unit step responsexis=1/sX0s =10ss2+65+5X0s =10ss+1s+5using…

Q: Find the general solution of the given system. dx =x +2y dt dy = 4x + 3y dt St -t+C2 2 a. e 1 b. St…

A: here we will find general solution of given system of equations,

Q: Consider the system of equations dæ = x(3 – x – 4y) dt dy = y(1 – 3æ), dt taking (x, y) > 0. dy = 0.…

A:

Q: 1. Let 1 A = 2 Y1 Y = Y2 -2 -1 -2e-t +2 G(t) = Yo = -2e-t +1 Write out the two equations that make…

A: Given:

Q: Find the complete solution using classical method to the system (D2 +6 D+ 25) y(t) = (D+ 3) x(t) for…

A: The system is D2+6D+25yt=D+3xt Initial condition is, y0+=0dydt0+=2Input xt=utTo find the complete…

Q: Solve the given system of DE's by systematic elimination. Dx + D2y = e3t (D+1)x + (D-1)y = 4e3t

A: to solve the system we need to first we need to use elimination method to find solvable equations.

Q: The process X (t) is WSS and Rz(7) = 58(7). Find E[Y²(t)] and Syy (w) if the system is described by…

A: Given: Rxxτ=5δτAndy'+3y(t)=x(t)

Q: Q: find x, y and z for the following system by using Gaussian Elimination Method and back…

A: The system of equation is given as 0.1x+y+2z=1y+2x=40.2x-0.125y-z=0 The augmented matrix is follows…

Q: b) Is the system with impulse response as below BIBO stable justify your answer h(t) = e2"u(-1 - t)

A:

Q: D2x+Dy=t

A:

Q: HW: Determine the response y(n), n20 of the system described by the second order difference…

A: Consider the second-order difference equation. y(n)-4y(n-1)+4y(n-2)=x(n)-x(n-1) The input is…

Q: H. W : Perform three iterations to approximate a root of the system described by * fi(x, y) = x² -…

A: Solution of given problem is given by using Newton Raphson method as follows :

Q: 1. Find y by Cramer's rule for the following linear system. x+0y+2z=6 - 3r+4y+6z= 30 -x-2y+3z=8

A: Cramer's rule:   for y= DyD where  | Dy | =Determinant of the matrix whose second row is replaced by…

Q: 2. Sõlve the linear system below w +x- 4z = -2 0.5w-0.5x + 2y + 0.5z = -2 -3x + 0.5y + z = -5 4w…

A:

Q: 4. Find the general solution for the system below (y, z are functions of t): y'= 3y + z, z'= 3z .

A:

Q: b) Find the step response for the system below d d di2 y (t) + 4¬y (t) +3 y (t) = r (t) c) Given the…

A: (b) d2dt2y(t)+4ddty(t)+3y(t)=ddtx(t) apply Laplace transform  s2Y(s)+4sY(s)+3Y(s)=sY(s) for an step…

Q: Determine the complete system responses, as per the type of system, governed by the following…

A:

Q: p = jp\p| (j=v-1). Write this as a system in R2 and find a nontrivial periodic solution.

A:

Q: ® Consider the linear system (3 X +2Y 3X + (6+t) y = 30 ) Determine aparticular value oft, so that…

A:

Q: Find the general solution of the given system. = 3x + 4y dy = 8x + 7y 11t (x(t), y(t)} = (C₁e¯¹ +…

A:

Q: For which value of a the system of ODES Ý1 = Y1+ ay2 + (e¯2¾ – 1), j2 = -ayı – Y2 has an unstable…

A:

Q: 6. The following system z0) - [ . z0) - [ %3D can be converted into an initial value problem of a…

A: `Given:  x't=3-2-34xt         1,        x0=1-2 Let xt=x1tx2t So, from (1) we get  x1't=3x1-2x2  ,…

Q: 3. Convert the following higher-order equation to system of first order equation :…

A: Given differential equation is y'''(t)+5y''(t)+4y'(t)+2y=2t2+10t+8,  With condition y(0)=1,…

Q: H. W : Perform three iterations to approximate a root of the system described by fi(x, y) = x2 - xy…

A:

Q: Use the method of undetermined coefficients to find a general solution to the system x'(t) = Ax(t) +…

A: First we will find the eigenvalues and eigenvectors of coefficient matrix A and form the general…

Q: dY = 3) Y, dt 3 (a) find the general solution; and (b) find the particular solution for the IC Yo=…

A:

Q: For the time-invariant system x' = Ax for which Ø(t) = eªt where: a. O b. C. d. a. Ø(t) = [Ø(t)]−¹…

A:

Q: Find the solution to the system that satisfies the given initial conditions. 0 2 x'(t) = x(t) + -13…

A: Hey, since you have posted multiple subparts, we only solve first three subparts of the question. if…

Q: ()- Write the given linear system in matrix form. Assume X = dx 3 -2х + Зу + е' sin(2t) dt -t dy =…

A: The matrix form of given system is given as follows :

Q: Consider the system described by the difference equation Yn+28yn+1 + 16y, = n4" + 3". Find the…

A:

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.