Consider the spring model %D where the linear part of the spring is repulsive rather than attractive (for a normal spring it is attractive). Rewrite this as a system of first-order equations in x and y = x'. x' = y' = Write down your system when you have it correct, for use in the next three problems. Then find all critical points and enter them below, in order of increasing x coordinate. (x,y) = ( ); (x,y) = (| ); (x,y) = (| %3D For reference for the next three problems, write down your critical points after you've gotten them all right.

Q: Sx+y= 1 (2х +у %3D 3 3. Solve the system for vectors in the field Z,.

A: Given: The given system is x+y=12x+y=3

Q: 111 I + 3y" + 3y + y = 0 How many linearly independent solutions would you need to find in order to…

A: given differential equation  y'''+3y''+3y'+y=0  here order of differential equation is 3.

Q: Solve the system d = dt with a1 (0) = 1 and æ2(0) = -1. %3D

A: The given system of differential equation: x1'x2'=   0-1-1   0 x1x2+t0  ;        x1(0)x2(0)=1-1

Q: Two chemical engineers, A and B, are working independently to develop a model to predict the…

A: Introduction: Suppose a model is to be constructed for a response variable, by using two explanatory…

Q: dK (t) The rate of net investment is given by dt (1 + 4t)e2t+4t + 12t/3 +t and the initial stock of…

A: we have to integrate with respect to t

Q: If y₁ and y2 are linearly independent solutions of ty" + 2y' + te³¹ y = 0 and if W(y₁, y₂)(1) = 4,…

A: Here given the differential equation as ty''+2y'+te3ty=0 or y''+2ty'+e3ty=0  ........(1)

Q: Let Y(t) = be the solution of , 6 1 Y, 5 4 -2 - Y' Y(0) 8 Write x(TT/10), round your answer to two…

A: To solve this problem first we write the system as a system of linear homogeneous differential…

Q: Consider the discrete-time dynamical system y+1 = v -3y +3yt. It has three équiibria, ) M*= 1, or y'…

A:

Q: Incorrect. If y, and y₂ are linearly independent solutions of t²y" + 2y + (5 + t)y = 0 and if W(y₁,…

A: We solve by using Abel's Formula.

Q: Q3- Solve the system of non-linear equations xy' +x = 12 x*y+4y = 1

A: The given problem is to find the solution for the given non linear equations. xy3+x=12 x2y+4y=1

Q: rewrite the following second order linear equation into of two equations. y'' + 5y' - 6y = 0

A: Given y''+5y'-6y=0

Q: Find all real values of the constants A and B for which the linear function F(r) • Ar + B satisfies:…

A:

Q: Q1. Solve the initial value problem of first order linear differential equation: x ௗ௬ ௗ௫ + y = e ௫ ;…

A: Introduction: A first order linear ordinary differential equation is expressed in the form of…

Q: The position of a particle moving along the y-axis is given by y(t) = ct³ + bt + 100, where c and b…

A:

Q: Q5. Write the governing equation of 1-D heat transfer with convective heat loss and indicate all the…

A:

Q: What is the stability of equilibrium points of A and B? Is the energy of B higher than A?

A: If the vector field lines converge to the point or stay close to a point at all times the point of…

Q: After extensive surveys, the research department of a company has determined that the supply and…

A: The supply equation is ,s(p)=500p-19500The demand equation is,d(p)=20000p

Q: There are three interconnected tanks, each with volume 10 liters and containing saline solution.…

A:

Q: Use the variation of parameters formulas to find a general solution of the system -3 2 et y' 2 -3 2…

A: The method of solving a nonhomogeneous linear system of differential equations is the following.

Q: A linear second-order non-homogeneous equation models this scenario: People falling at a height of…

A: The objective of the question is to determine the initial conditions of the height y(t) of the…

Q: W = 0.3RX +0.7Ry, where Rx is the stock return from investing in stock X and Ry is the sto investing…

A:

Q: (a) If b² – 4ac = 0 and y1 = em# solves ay" + by/ + cy = 0, use reduction of order to get a linearly…

A: Q2 a) Let y=uy1y=uemxy'=u'emx+umemxy''=u''emx+2u'memx+um2emxPutting the value in equation, we get…

Q: Use Newton-Raphson method to solve the system x* + y – 1 = 0 y* – x +1 = 0 with the starting value…

A: We will use the following Newton-Rapson formula for finding the roots of 2 variable equations.…

Q: 94: For the system presented by the function x +y+ 2 4xy. Calculate all the possible points at which…

A:

Q: If y = x2 is one solution of x2y''+2xy'-6y=0 and the other linearly independent solution.

A:

Q: [o1] Write the following system X' = X - 2 3 X (0): %3D as a second order D.E , then solve it .

A:

Q: Find a root of the system of non- linear equations x +y = 3; xy 1 by Newton's method starting with…

A: here we need to find the root of given equation using newton's method. the solution is following.

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: f(x) = e−x,    n = 5

A: Given:          fx=e-x ,n=5 A Maclaurin series is given by fx=∑n=0∞fnan!xn Here fx≈Px=∑n=05fnan!xn…

Q: Match equations y′ ? 1 − x, y′ ? x − 2y, y′ ? x(1 − y) to slope fields. Justify

A: The plot of y'=1-x is as follows,

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.