he equilibrium pul 12) P(x) = -2x + 8, S(x) = 3x + 2 %3D

Q: 4. For y' = y3 +y² – 6y, Find the critical points. Draw a phase diagram and mark the critical points…

A: Given y'=y3+y2-6y Given a differential equation y'=fy a point y0 is said to be a critical point if…

Q: X~N(22,3) find maximum of x in bottom quartile

A:

Q: Q2. Solve the initial value problem 2- y = f(x) with initial condition y(0) = 2 and dx (0, 0<x<1…

A: Given differential equation is. dydx-y=fx                                      ........1 The given…

Q: 2. To the discrete population model for P with constant birth and death rates add a constant…

A:

Q: (c) Hence determine the type and stability of the equilibrium point Xe = 0. (d) Solve the initial…

A: Given :                 dxdt =1447x    ,   x0 =21 To find  : type and stability              : solve…

Q: 6. Find the general solution of the system: :) *+(- sint X = -2 cost

A:

Q: 2x-5 2). S -2x-3x dx (Integration by Partial Fraction)

A: The given integration,∫2x2-5x3-2x2-3xdx

Q: Q1// Use Tow Phase method to solve the Mathematical model (Stop at Table 1 in Stage Two) MinZ…

A: The given LPP is, Min Z= x1-2x2s.t.       x1+x2≥2          -x1+x2≥1                   x2≤3and…

Q: 2) A: By using partial method solve [2x² cos x dx

A:

Q: y=3 is an equilibrium solution for the d.e. y'-y=3 Select one: True O False

A: We have to check

Q: • Consider the (nonlinear) initial value problem / = -2y, y(0) = yo Does it have a solution for a)…

A:

Q: 1. S 4x-5 dx - partial fraction 2x2 +4x-6

A:

Q: When solving a particular boundary value problem using the approximate solution (x)=x-1+a1 (x2-6x)…

A: At the collocation point the residual function should be 0, that is, here R(x=3) should be 0.…

Q: netimes a constant equilibrium solution has the property that solutions lying on one side of the…

A:

Q: Solve partial DE  Py-q2x2=x2y

A:

Q: Use Gauss-Seidel method to solve for x, X,, Xạ until the relative error falls below 5% Repeat with…

A:

Q: Q/ If the equilibrium point is the origin of the nonlinear system, then the Libanov function can be…

A: Given,Condition about " Libanov function" to check the stability of the non-linear system.

Q: p' = rP a where 0 < a< K and r is a positive constant. Identify all equilibrium populations and…

A: We will find equilibrium points by equating P'=0 then depending on sign of P' draw phase diagram and…

Q: 11. f(x) = x² + 7x + 10 Opens up/down: Vertex: Axis of symmetry: Solution(s): y-int:

A:

Q: 22-12x To solve dx, partial fraction is to be employed. What is the most appropriate form of the…

A: The partial fraction decomposition method is used to simplify the calculation of integral. When the…

Q: 2x2-5 2). S: x3-2x2-3x dx (Integration by Partial Fraction)

A: Solving the problem by doing the integration.

Q: 3.Given a nonlinear equation y = 3x^3-

A: Given,       y=3x3-5.12x2+3.4x-1.9

Q: se Newton-Raphson Method to find the approximate solution of the nonlinear equation f(x) giv en as…

A: To approximate the solution of the below equation using the Newton-Raphson Method. x3−x−1=0

Q: e) y-2y'+y

A:

Q: 5. The function h(x) = x² + bx² + d has a critical point at (4, -20). Determine the constants b and…

A: This question is related to the application of derivatives.

Q: (a) Show that there are two possible equilibrium values for p in [0,1] (which you should calculate)…

A: We have, dpdt=cp1-p-p2 For the equilibrium point we have, dpdt=0cp1-p-p2=0pc1-p-p=0p=0or…

Q: C Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains 100 L…

A: We will use the fact Rate of change = Rate in - Rate out  to find differential equation for amount…

Q: A reversible chemical reaction 2A + B = C can be characterized by the equilibrium relationship, Cc K…

A: False Position Method:- For a function f(x) the root is x2=x0 fx1 - x1 fx0fx1 - fx0 Given that  K =…

Q: (a) Starting from the initial trial solution (x1, x2) = (0, 0), apply the gradient search procedure…

A:

Q: linearize the nonlinear equation in the region defined by 4 < x < 5, 3 < y < 4 z = y?Vx + 5e(3x-y²)

A: Given, z=y2x+5e3x-y2 The goal is to linearize the given equation around the operating point,…

Q: 2 b. y" + y' - 2y = %3D

A:

Q: tank contains 200 liters of brine in which there are 3 kg of salt per liter. It is desired to dilute…

A:

Q: Find the number of units x that produces the minimum average cost per unit C in the given equation.…

A: given

Q: Part II Solve the initial value problem. b. 3y(x?- 1) dx+ ( x³+ 8y– 3x) dy=0 y (0) = 1

A:

Q: (a) Write the general solution. (b) Classify the critical (equilibrium) point (0,0). (c) Sketch the…

A: This is a problem of critical point analysis. Stability analysis.

Q: 2. (20 points) Solve using integrating factors method. xy'-3y=x, y(2)=1.

A:

Q: Q-3- Eilaluate #the fallowing Integration x²-1 x² 1- x3 2 2.

A:

Q: equilibrium

A:

Q: 4. (a) dzy Solve: dx2 + ( = 0. (b) Solve xy" + (1 – x)y' – 2(1+x)y = e-*(1 – 6x) by the method based…

A: We have, d2ydx2+dydx+dydx3=0 ..i Put dydx=v ⇒d2ydx2=dvdx Now substitute in equation i we get…

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

A:

Q: |Using VIM to solve y" + 2y² = 0, y(0) = 0, y'(0) = 1 %3D variational iteration method

A:

Q: 7. State whether the equation is ordinary or partial, linear or nonlinear, and give its order. * ()…

A:

Q: Find the optimal solution of the Linear Pr problem below using two phase method. form first and then…

A: Simplex method: The simplex approach is a method for systematically evaluating vertices as potential…

Q: d?x 4. Solve the IVP: dx 4. dt + 4x = t³e2t,x(0) = 0 ,x'(0) = 0 by any method - dt2

A:

Q: (c) Suppose that two of the pipes become blocked so that x3 = 0 and x1 = 0. Determine the flow rates…

A: Topic - flow diagram

Q: lution of the initial value problem written below by using reduction of order method. y"-2y'+10y=0,…

A:

Q: t+Vt2 - 36 In dt 3. + C t2 -36 6

A:

Q: solution of the given initial value problem is certain to exist. (25 – t) y/ + 2ty = 8t², y(-8) = 1…

A:

Q: Suppose a population is modeled by the equation P+1 = aP;e¯rP. where a and r are positive real…

A: ANSWER :