cted to one another with rates of flow r12 = 4, r21 = 3, r13 = 2, r31 = 3, r23 = 6, and r32 = 5 (rij denotes the rate of flow from tank i into tank j), all in liters/sec, and volumes V1 = 5, V2 = 10, V3 = 15, all in liters. I nitially x1(0)=0, x2(0)=20, x3(0)=40, all in grams (of salt). Find the amounts of salt x1(t), x2(t), x3(t) in the three tanks as t goes to infinity.

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A: There are 4 interior and each adjacent to 4 other points.

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A:

Q: we consider the system 2r + 2y z+ 3y. dt For the given function Y(t) = (r(t), y(t)), determine if…

A: Since you asked for part 1, so I solved only part 1.

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A:

Q: H. W: Perform three iterations to approximate a root of the system described by fi(x,y) = x² – xy +…

A: We have to find solution by using Newton's Raphson Method.

Q: 8. Consider the linear system Mv = y where 1 01 М— |1 1 1 1 v1 V = y = U2 6

A:

Q: Use operator / elimination method to solve the given system dy 2.x + 2y + 1 dt dx dt dx dy + 2 dt y…

A: Given system is dxdt+dydt=2x+2y+1           (1)dxdt+2dydt=y+3                    (2) let the…

Q: Pls explain to me step by step. pls dont skip any steps. thanks

A: To analyze the given non-linear system using the relevant theorems

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A:

Q: We can use the Cramer's rule for the following homogeneous linear system to get x = y = z = 0 as one…

A: To find out the true or false.

Q: Use the method of undetermined coefficients to solve the given nonhomogeneous system. dx/dt = 2x +…

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A:

Q: dri(t) dt = 11 + 12 + 3r3 = 2r2 + 2r3 1. Solve the homogeneous linear system of D. E. (S) dt dt

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A: According to our company policy, we are supposed to answer only first question. For the rest please…

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Q: Write a program that uses Newton's method to obtain a solution of the system of nonlinear equa-…

A:

Q: ) Write the IVP y" + 4y = 9 cos t, y(0) = 3, y'(0) = 4 as a system of first order ODES in terms of…

A: Given :-  The IVP  y'' + 4y = 9 cos t                 , y (0) = 3 , y' (0) = 4

Q: Find the general solution of the given system. dx = 3x+4y dt dy = 8x+7y dt (x(t), y(t)) =

A:

Q: Use variation of parameters to solve the given nonhomogeneous system. dx 2х - у %3D dt dy = 3x – 2y…

A:

Q: Consider the boundary value problem y" = y+ y(1) = 1, y(3) = 2. Solve this system over the interval…

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A: Solve the given system of equations:2x'+y'-3x-4y=e-tx'+y'+3x+y=e4t

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A: For a system of equation to be non trivial, it should have infinite many solutions. This is possible…

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A:

Q: Consider the Sturm-Liouville system y" + 2y + (1+)y = 0, y(0) = 0, y(L) = 0; 0 0 is a non negative…

A: Given the Sturm-Liouville problem y"+2y'+1+λy=0, y'0=y'L=0, 0<x<L. Also, λ≥0 is a non-negative…

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A:

Q: H. W : Perform three iterations to approximate a root of the system described by * fi(x, y) = x² -…

A: Solution of given problem is given by using Newton Raphson method as follows :

Q: Use the method of undetermined coefficients to solve the given nonhomogeneous system dx 5x + 9y + 3…

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Q: Consider the homogeneous system Ax = 0, where A is n × n. If A is nonsingular, show that the only…

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Q: Find the general solution of the given system. dx Зх + 4y dt dy 8x + 7y dt (x(t), y(t)) =

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Q: I. Find all the values of d for which the homogeneous lihear system has nontrivial solufions (1-8) x…

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Q: Find the critical points of the system mentioned in the Attachment.

A: The system is given as, dxdt=14x-2x2-xy  , dydt=16y-2y2-xy To find the critical points of the…

Q: ® Consider the linear system (3 X +2Y 3X + (6+t) y = 30 ) Determine aparticular value oft, so that…

A:

Q: Find the general solution of the given system. dx = 9x - y dt %3D dy = 5x + 5y dt (x(t), y(t))

A:

Q: dx dt dy dt = 1 6 (x−1)(5−x− 6y x ) = y 20(1− y x−1) Find the nullclines  of the system

A:

Q: we consider the system dz = 2r + 2y dt =I+ 3y. dt For the given function Y(t) = (z(t), y(t)),…

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Q: Use variation of parameters to solve the given nonhomogeneous system. dx 2х - У dt %3D dy Зх — 2у +…

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Q: H. W : Perform three iterations to approximate a root of the system described by fi(x, y) = x2 - xy…

A:

Q: A system of particles are located on the x-axis with masses (in kg) 7, 12, 2, 10, and 3 whose…

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Q: Find the general solution to the homogeneous system of DE: -3 x' = Ax where A = 3 15 -3 3 18

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Q: Solve and find the response of a linear second-order system described by (dy^(2))/(dt^(2))+3…

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Q: Find the general solution of the given system. dx 9х — у dt dy = 5x + 5y dt %3D (x(t), y(t))

A: Given

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A:

Q: H. W : Perform three iterations to approximate a root of the system described by fi(x, y) = x2 -…

A: To Determine :-  To approximate a root of the system of non- linear equations are : f1  x , y  = x2…

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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.