KK Suppose 42 7(t) = cet + ze? -3 -2 -1 -3 -2 -1 -1 ý(1) = -3 A В (a) Find c, and c2 . y2 1/2e 1 yi -e/2 -3 -2 -1 -3 -2 C2 -1 -1 -2 -2 -3 -3 (b) Sketch the phase plane trajectory that satisfies the given initial condition. Which graph most closely resembles the graph you drew? D (c) What is the approximate direction of travel for the solution curve, as t increases from -o to +o? OA. along the line y = -x toward the origin and then along the line y = x away from the origin

Q: 3. For the competing species population model dx —D х(-х — Зу + 150) dt dy %3D У(-2х — у + 100) dt…

A:

Q: Find the solution. (D² - 20 - 3)y = 0; when x = 0, y = 0, y'= 4 A y = e-e B y =e+e y = e y = -e

A:

Q: (b) Find a particular solution of y"+9y+20y=6e-5x

A: Particular solution is  −6xe−5xExplanation:

Q: 2. Find all solutions to the equation y" +y – 10y = 0. Hint: p(A) = X3 + A – 10 = (X – 2)X² + 2A +…

A: The solution of homogenous linear differential equation of constant coefficient is find by…

Q: x(t) = Find real-valued closed formulas for the trajectory x(t + 1) = Ax(t), where A = 4- [12 -13]…

A: Step 1:  Step 2:

Q: x(t) = Find real-valued closed formulas for the trajectory x(t + 1) = Ax(t), where A = = [12 -12]…

A: The answer is given belowExplanation:Step 1: Given x(t+1)=Ax(t) , where A=[−912​−12−9​] Step 2:Step…

Q: (b) Consider yı and y2 as two solutions for the following DE where yı = x-1 and the Wronskian of the…

A: b Given differential equation is y''+pxy'+qxy=0.......1. And y1, y2 be the two solutions of the…

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.