Solve the following system: x'₁ (t) = −x₁ (t) + 2x2 (t) + 2x3 (t) — 2 x' (t) = 2x₁ (t) + 2x2 (t) + 4x3 (t) x' (t) = 2x1 (t) + 4x2 (t) + 2x3 (t) + 1.

Q: Consider the system described by * = Ax, where, A = [1] Suppose x₁ (0) = 1 and x₂ (1) = 2. Find…

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Q: Solve X x (t) = y(t) = - 17 ²7] [7] (0) - x (0) = 4, y(0) = 19

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Q: Solve the linear system by Variation of Parameters x' = Ax +b, A= -1 b = x(t) = 2

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Q: X' = [ x -2 %3D -1 -4.

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Q: A firm’s revenue after selling q items is given by R(q) = 2q3 +36q while the firm’s costs after making…

A: R(q) = 2q3 +36qC(q) = 3q2 −10Profit, P(q) = R(q) - C(q) = 2q3 +36q - (3q2 −10) = 2q3 - 3q2 +…

Q: Find the general solution of the given system of equations. 6 -1 - (₁5¹) x + (²) X 35 -6, x(t) = X'…

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Q: Solve the following system: - x' (t) = -x₁ (t) + 2x2 (t) + 2x3 (t) — 2 x' (t) = 2x₁ (t) + 2x2 (t) +…

A: We solve by using eigenvalues and eigenvectors.

Q: solve: x= 3x+y+z+1-3€ -4²-4³ g' = 2x+4y +az-4t²-at² Lz'= x+y +3z + 121²-3³ 9 Hint: (x₁4₁)= (t.t²,…

A: Actually given hints is the particular solution, although i deduce this by undetermined coefficients…

Q: Use the method of undetermined coefficients to solve the nonhomogeneous linear system *-[1]+[+] X -t…

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Q: Solve the difference equation: 3 (²7) y[n+ 2] - n> 0 y[0] = 10 and Y y[n + 1] + y[1] = 4 n (1) ₁…

A: Given difference equation is ,      yn+2-32yn+1+12yn = 14n   ;  n≥0     ;  y[0]=10  and  y[1]=4 (.)…

Q: Reduce the equation yzxx + (x + y)2xy + XZyy = 0 to a canonical form and solve it.

A: The characteristics integrals:

Q: Find the solution of the system of equations below: X; x(0) = (²) x' = (²-3)x;

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Q: solve: x= 3x+y+z+1-3t-t²-t³ g' y = 2x+ay+az-4t² - et 2'= x+4 +37t+2+²-3+³ Hint: (x, y, z)= (t.t²,…

A: Using matrix method

Q: Use the linear method to solve: xy' - 6x²y = 3x²; y(0) = 3

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Q: For the following system, find x₁ (1) + x₂ (1). x₁ (t) = 3x₁ + 4x2 x₂ (t) = 3x₁ + 2x2, x1(0) = 2,…

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Q: Two balloons, one red and one green are released from a platform at t=0. Each balloon goes up for a…

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Q: 1 Find the solution to (2x+3) y'=y+ (2x+3) ²; x = -1;y=0 1 2y = (2x+3) 2 In (2x+3) In(2x + 3) 3 y=…

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Q: Does the following system of equations have a solution? How do you know? s(x)=x^2(1/9x+2) and…

A: We need to graph both the functions for set of solution

Q: The cost per day to society of an epidemic is C(x, y) = 40x + 230y where C is in dollars, x is the…

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Q: Verify that V = x14+ 2x22+2x1x2 + x12 is a Lyapunov function for the system described by the…

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Q: Anna and Bob are the only residents of a small town. The town currently funds its fire department…

A: Ans:

Q: -1 -1 3. Find a particular solution of x' = -2 2 x+ 4 -1 -2 et

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Q: 5. Given: f (x) = ax³ – 9x² + 2x – 4 and g(x) = bx³ – 5x² + 62x + 70 | Solve for all values of a and…

A: We have to find

Q: Solve the system of linear equations with the given initial conditions. x' (t) = [1 2] x |x(t) with…

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Q: Find the values of a, b, c, and d when f(x) = ax3 + bx2 + cx + d and the following conditions are…

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Q: With profits from an Apple orchard is given by P(x)=x(404−2x) dollars, where x is the number of…

A: Given :-Profit function isP(x) = x (404-2x) dollarswhere x is number of almond trees per acreWe have…

Q: Solve the system using the elimination method 5x'+y" -y + =t x" - 4x - 2y' = -2...

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Q: 2.) f(x) = 2x + 4x + 2x + 1 %3D 31 2 g(x) = x - x + 7x +9 Find (f + g)(1)

A: Topic - functions

Q: (2) x (x+3)y"+2y'+y=0 solve for yox)

A: To solve the differential equation: x(x+3)y''+2y'+y=0 We can start by assuming a solution of the…

Q: What is the solution of (2x - y)dx + (4x + y– 6) dy = 0? а. (x+у-3)°- с (2х +у- 4)? b. (x-y+3)²=…

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