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

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

A:

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: 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.