1. Let 1 A = 2 Y1 Y = Y2 -2 -1 -2e-t +2 G(t) = Yo = -2e-t +1 Write out the two equations that make up the system Y'(t) = AY(t) + G(t), Y(to) = Yo. The true solution is Y(t) = [e-t, 1]".

Q: ) Find a particular solution to the system of equations x' = 168z + 105y + 3t, y' =-280r - 175y + 5.…

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Q: X' = 2 4 4 -1 -2 0 X -1 0 -2,

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Q: Suppose we solve the linear system Ax = 2.00 1.00 [ ] x = [ 1.99 1.00 Cz= 1.00 -1.00 Now suppose…

A: As per the question we are given two equivalent system of linear equations in matrix form as Ax = b…

Q: x' = Solve y"-5y'+6y=0 by writing it as a system Ax and solving that system.

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Q: 3. Linear Systems (a) ii. iii. i. For the following systems, find the general solutions: x' = 10y,…

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Q: Write the given system as a set of scalar equations. Let x' = col (x1'(t), x2'(t), x3 (t)- 0 1 0 1…

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Q: Find the real-valued solution to the initial value problem Jyí 3y1 + 2y2, Y₂ -5y₁ - 3y2, Use t as…

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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: Solve the system x' = 22+2y y' = -4x+8y-4z = 2z with initial conditions, r(0) = 5, y(0) = 7, and (0)…

A: We use the Laplace transform to solve the given system

Q: Transform the given equation into a system of first order equations (x-1)y(4) + (x+1)y'' + (tan x)y…

A: We need to transform the given equation into a system of first order equations.

Q: [ -1 + dt X2 with x1(0) = 1 and x2(0) = –1.

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Q: AMBK Company manufactures furniture such as sofas and tables. In their current inven- tory, a total…

A: Each sofa need 4 plank of wood Each table need 2 plank of wood Total availability of wood 48 plank…

Q: #12 Compute the quantity, wow.)w, 4 Using W= (ww )= [8] 2 7 Typeintegers or simplified fraction.

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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: Write the given third order linear equation as an equivalent system of first order equations with…

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Q: Figure 1 shows a periodic function, f(x), with period of 2. f(x) –π ο π 0 W Figure 1 24 X f(x)= (a)…

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Q: Find the solution to the given system that satisfies the given initial condition. x' (t) = (a) x(0)…

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Q: 3. Find the values of x and y that solve the system of equations (assume x ≥ 0 and (a) xy = 4 and…

A: We have to find the values of x and y that solve the system of equations (assume x≥0 ) a xy=4 and…

Q: 3 ve the nonhomogeneous system tY' = (²2 =²) x + (-²₁) -21). Y (2-2)

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Q: Use Newton's method with x(0) = 0 to compute r(3) for each of the following nonlinear systems.…

A: The Multivariate Newton Raphson method uses the formula below to perform the iterations .…

Q: 2) Find the General Solution of the System of Equations. [1 1 1 X' =|2 1 -1X 0 - 1 1

A: The given equation is X'=11121-10-11X.

Q: 2. Solve the system using Newton's method (absolute error ɛ = 0.0001 ). x + x = 1 2x,-2 e -x, = 0

A: I have appended the formula used in the solution part

Q: e the method of undetermined coefficients to solve the given nonhomogeneous system. *-(:)** (*:)*…

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Q: Find C so that y(x)=C(1-x2) a.  y(2)=1 b.  y(1)=2

A: To find the value of C so that y(x)=C(1-x2)...(1) with the given initial conditions.

Q: Write the system given system of differential equation in matrix form. Y₁' = 3y₁ + y2 + 3 sin(4x) Y2…

A: Given, system of differential equations,

Q: Consider the system of differential equations Y1 + 3y2, %3D 3y1 + Y2, %3D with solutions Y1(t) Y2(t)…

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Q: 2. Let ([0, 1], L, m) be a Lebesgue measure space, and let A be a nonempty measurable subset of [0,…

A: Given: Lebesgue measure space is 0,1, L, m.A is a measurable non-empty subset of 0,1. Ek Lebesgue…

Q: U₁ + Ux+Vx = 0, v₁ + UxVx = 0, u(x, 0) = u(x), v(x,0) = vo(x).

A: Given clear explanation below.

Q: Convert the following linear equation into a system of first order equation of the form y' = P(t)y +…

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Q: The break-even point occurs where the graphs of C and R intersect. Thus, we find this point by…

A: Given, Cx=500,000+400xOr  y=500,000+400x         ......1Rx=600xOr  y=600x…

Q: Find the general solution of the fourth order linear equation y(4) + 4y" + 4y = 0.

A: Given problem is :

Q: Use EROS and backward substitution to solve the system Ax b, where 1 2 2 1 1 1 and b = 1 -3 -1 What…

A: We have to solve the system of equations.

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.