7. A scientist places two strains of bacteria, X and Y, in a petri dish. Initially, there are 400 of X and 500 of Y. The two bacteria compete for food and space but do not feed on each other. If x = x(t) and y = y(t) are the numbers of strains at timet days, the growth rates of the two populations are given by the system x' = 1.2x – 0.2y, y' = -0.2x + 1.5y Determine what happens to these two populations by solving the system of differential equations.

Q: Consider a linear birth process starting from X(0) = 2 with birth parameters An = ß. n where n = 1,…

A: Let a linear birth process starting from  with birth parameters  where .

Q: Consider the system a = x1 + x2 a = 4x1 – 3r2 with initial conditions a1(0) = 1 and r2(0) = 2.…

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Q: nonhomogeneous system.

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Q: The systems of equations are x_1 = -5x1 + x2 and x_2 = 4x1 - 2x2

A: The objective of the question is to find the values to which x1(t) and x2(t) converge as time t…

Q: Two species X and Y live in a symbiotic relationship.That is,neither species can survive on its own…

A: Given, the system is We have to determine the populations x(t) and y(t). and initial conditions are…

Q: Solve the initial value problem (1+ x²)y" + 4y = 0, y(0) = 0, y'(0) = 12. If the solution is y = k=0…

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Q: solve the given initial-value proble x1'=2x1+x2, x2'=-x1+4x2, x1(0)=1, x2(0)=3

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Q: n each of Problems 1 through 8, express the general solution of the given system of equations in…

A: Given system is x'=-76-6-95-90-1-1x Let A=-76-6-95-90-1-1 Let the eigenvalue of A be λ. Then…

Q: What are the critical points of the following system and how do you find those points? x'=7x-xy…

A: Given system is  x'=7x−xyy'=5y+x2 For critical point equate x'=0 and y'=0 Hence, x'=0…

Q: Solve the system of differential equations 'x'= 3x - 3y y = 0x + 4y x(0) = 0, y(0) = 1 x(t) = y(t) =

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Q: I1 x₂ = x3 = || Solve the following initial value problem: 2 -10 7 +-60-~-() -1 5, z (0) 0-10 9 d dt…

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Q: Q1. Consider the following batch chemical system which we wish to model similarly to A=B-P The time…

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Q: If the solution to the initial value problem y' + ay = 0, y(0) = b passes through the points (2, 2)…

A: Given data

Q: Find the particular solution. y(x): = e* ý =4(2 +2) g®, y(0) = 1 *9

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Q: Solve the system dx dt x(0) with the initial value 0 1 [B] [8] = -12 5 x(t) = = -30 13 x

A: Given system of ODE  with initial value..We have to find a solution to the given system.

Q: 4. Solve the non-homogeneous systems of ODEs x' = Ax+f(t), with x(a) = xa using the given matrix…

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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.