Q1/ By using Gauss-Seidel method , find the solution of the system when the initial value is X) = 0, e= 0.005 %3D 5x + 2y – z = 6 x + 6y – 3z = 4 2x + y + 4z = 7

Q: given that (x,y) > 0, find the equation for the non-zero x nullcline and y nullcline. What are the…

A: Consider the given equations:  dxdt=x1-x2-y and dydt=y1-y3-x

Q: i(t) = y – x³ ý(t) = -x³ – y3 a) Is the origin stable or asymptotically stable for the linearized…

A: (a) Given equations are, To find the stability, And,

Q: Find the general solution of the system using the elimination method. a' + y +2y = sint r' - x + y –…

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Q: . Consider the linear system dY 2 Y dt -2 (a) Find the general solution. (b) Find the particular…

A: The given differential equation is  dYdt=02-2-1Y The general solution of this equation is…

Q: Use variation of parameters to solve the given nonhomogeneous system. X' X(t) =

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Q: 2х — 8y + 5z 3D-5 2х + у —z%3D12 — 5х + 3у + 9z 3-17

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Q: Use Euler's method with step size 0.5 to compute the approximate y-values y1 Y2 Y3 and Y4 of the…

A: Given :y'=y-5xy(3)=0

Q: Consider a seesaw with two children of masses ml and m2 on either side. Suppose that the position of…

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Q: Use variation of parameters to solve the given nonhomogeneous system. X' = -7t e X(t) =

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Q: What is the long term behavior of the solution with the initial condition (-2, –1)? -3

A: Since, at point x=-2 and y=-1 present in the graph having the phase portrait curve as decreasing to…

Q: Identify if its:       a. Homogeneous DE,       b. Exact DE,       c. Linear DE of order one and…

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Q: Find the general solution to a homogeneous, linear DE with constant coefficients

A: In this question, we need to find the solution of a homogeneous linear differential equation with…

Q: 4xyy’ = y^2+x^2 y(1)=1  find the specific solution of the initial value problem

A: We will solve the problem.

Q: 3. Using Jacobi Method, obtain the solution to the system 21 + 522 + 33 = 30 3x1 + 7x2 + 13x3 = 80…

A: Let us solve the system of linear equations using Jacobi Method in the next steps.

Q: X(0)=5; y(0)=-1. dx = 3x - 2y dt dy = 2x + 3y dt

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Q: Given the system of nonlinear DEs r' = -2x – 3y + xe and y' = 3.x – y+2 – 2e: (a) Linearise the…

A: Given: The given system of non linear differential equations x'=-2x-3y+xey and y'=3x-y+2-2ey

Q: Consider underdamped forced system governed by y′′ +y′ +3y = 4cos(3t). (a) Find the solution…

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Q: Given the system of nonlinear DEs a' = -2x – 3y + xe" and y'= 3x - y +2- 2e": (a) Linearise the…

A: Given nonlinear system of differential equations is dxdt=-2x-3y+xeydydt=3x-y+2-2ey Let P1x, y=xey…

Q: 4. For which values A ER has the system 8z - 3z - 6y = dx 21 + y+ 4z = y 4r + 3y + z = Az infinitely…

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Q: Consider the initial value problem y' = y(2-ty), yo = y(0). Observe that for yo = 0, y = 0 is an…

A: Given, initial value problem is: y'=y(5-ty) with y0 =y(0) and equilibrium solution for y0=0 i.e.,…

Q: What is the solution to the initial – value problem : 4x?y" + 4xy' – y = 0 with y(4) = 2 and y'(4) =…

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Q: The system æ' = 4x², y' = 5y? has an isolated critical point at (0,0), but the system is not almost…

A: Solve the system        x'=4x2       y'=5y2

Q: Consider a seesaw with two children of masses ml and m2 on either side. Suppose that the position of…

A: We plug the given values in the given formula.

Q: What is the solution to the initial – value problem : 4x²y" + 4xy' – y = 0 with y(4) = 2 and y'(4) =…

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Q: Consider underdamped forced system governed by y''+y'+3y = 4cos(3t). Find the general solution of…

A: We will find out the required solution.

Q: Suppose the homogeneous linear system i = Ax has general solution x() = qc [:] + c«* [ i ]. + c2e…

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Q: P2 Find all equilibrium points for the system 1) x"+(x') +2x = 0 x' = sin y 2) y' = e*- -1 And

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Q: 1. a. Solve the system y = y1 + 4y2 y2 = 2y1 + 3y2 b. Find the solution that satisfies the initial…

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Q: Use the method of variation of parameters to find a particular solution of the DE (3x – 1)y" – 9xy'…

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Q: Use variation of parameters to solve the given nonhomogeneous system. X' X - -7t e X(t)

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Q: Use variation of parameters to solve the given nonhomogeneous system. x-(E) et e2t X' = 1 6. te 6t…

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Q: Recast the higher order initial value problem into an initial value problem for a system of first…

A: We recast the higher order initial value problem into an initial value problem for a system of first…

Q: Using (a) Jacobi Iterative Method and (b) Gauss-Seidel Method, obtain the solution [12x +3x, – 5x,…

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Q: Q3 Given the following non-homogeneous system of first-order linear differential equation: yi' = 5y,…

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Q: In determining the concentration of a chemical in a system consisting of two compartments separated…

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Q: - Ay A 3 1 -2 221 a-) Find a generol solution of the system ? 6-) Find a porticular solution of the…

A: Consider the given system of equation.

Q: 2) .. Use separation of variables to find the general solution.   dy dt − 12t3e−y = 0.

A: Answer: The solution is as given below:

Q: Find the general solution of the system of equations {dxdt= −5x − 8y {dy/dt= 4x + 7y. Use your…

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Q: Consider the system dy = Y1 – 2y2 – 2e¬t + 2 dt dy2 2y1 – 42 – 2e-t +1 dt with initial values y1 (0)…

A: The given system of differential equations are as follows: y1'=y1-2y2-2e-t+2y2'=2y1-y2-2e-t+1 Let…

Q: Consider the system {{ = - sin(x) (a) Find all the critical points (equilibrium solutions). (b) Find…

A: (a) Given system of equations are dxdt=y and dydt=-sinxthat is X'=AX where A=01-sinx0Critical points…

Q: Using Gauss-Seidel Method, obtain the solution to the system; x1 + 5x2 + 3x3 = 30 %3D 3x1 + 7x2 +…

A: Given that,x1 + 5x2 + 3x3 = 303x1 + 7x2 + 13x3 = 8012x1 + 3x2 -5x3 = 2 Initial Approximation is…

Q: Use variation of parameters to solve the given nonhomogeneous system. 1 1 et o x + X' =| 1 e2t te 6t

A: Solve the given nonhomogeneous system               X'=110110006X+ete2tte6t using variation of…

Q: The next two questions refer to this scenario. Consider simulating the system of equations da - 2x,…

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Q: Use the Gauss-Seidel method to find approximate solutions to -2x1 + 10x2 - 2x3 = -30 T1- 2x2 + 15x3…

A: To find the solution of the system of equation by Gauss Seidel method idf the system of equation id…

Q: Q3 Given the following non-homogeneous system of first-order linear differential equation: yi' = 5y,…

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Q: Solve the initial value problem using any method and demonstrate that the solutions to homogeneous…

A: Suppose we have differential equation where a,b and c are constant real number .Then solution of…

Q: 2. Using Gauss-Seidel Method, obtain the solution to the system X1 +5x2 + 3xX3 = 30 3x1 + 7x2 + 13x3…

A: The coefficient  matrix is 1 5   33 7  1312 3-5, now this matrix is not diagonally dominant, we can…

Q: The population dynamics for prey-predator model of owl and rat is representated by follow- ing…

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Q: A two-dimensional rectangular plate { (x, y): 0 < x < 1,0 < y < 1} is subjected to the temperature…

A: According to the given information, A two-dimensional rectangular plate is subject to temperature at…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: