You are given the following inhomogeneous system of first-order differential equations for x(t) and y(t) in matrix form: x ̇ = 2 x + y + 3 e t, y ̇ = 4 x − y . Write down the complementary function for the system of equations and then find a particular integral for the original inhomogeneous system. Please explain each step

You are given the following inhomogeneous system of first-order differential equations for x(t) and y(t) in matrix form: x ̇ = 2 x + y + 3 e t, y ̇ = 4 x − y . Write down the complementary function for the system of equations and then find a particular integral for the original inhomogeneous system. Please explain each step

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Sx+y= 1 (2х +у %3D 3 3. Solve the system for vectors in the field Z,.

A: Given: The given system is x+y=12x+y=3

Q: Convert the second order ODE x''=sin(2t)x'+4tx to a first order system of two equations. Use y for…

A: Given the second order differential equation x'' = sin 2t x' + 4tx --------(1)…

Q: Do two steps of the Newton's iteration for solving the system of nonlinear equations: u? + 2uv = 1…

A: Given system of non linear equation is u2+2uv=1(u-1)2+v2=1 with initial guess x0=u0v0=-11 Let…

Q: Consider the IVP: y'' - 2y' - 3y = 0, y(0) = 0, y'(0) = 1 Find two linearly independent solutions…

Q: [4 .3) Use the exponential method to find the FM for the system: y' = 0 Lo -2 4 0 01 -2 y 4]

Q: Consider the dynamical system Yk+1 = log (yk) + Yk- Which of the following statements is true about…

Q: The Bernoulli equation y'+37 xy'= 34 y can be converted to one of the following linear equations: a.…

Q: Find all equilibrium points for the following system of equations: x' = x-y+4 y'=3x-y+1

Q: Question 6. Find the solution to the following system of equations and show that the solutions you…

Q: Please answer all and graph

Q: Find the general solution of the given system of equations. Solve using similarit transforms. x' =…

A: Given, x'=2-13-2x+1-1et

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. Describe each of the following equations, giving its order and telling whether it is ordinary or…

A: 1)Given DE is y"+3(y')2+4y=0. We find it's order and decide whether it is ordinary or partial and…

Q: rewrite the following second order linear equation into of two equations. y'' + 5y' - 6y = 0

A: Given y''+5y'-6y=0

Q: Evalutate: limx→5 O-2 04 05 x-5 √x-1-2

Q: (6xy)dx + 4y +9x ² )civ = 0

Q: Show that the following system is exact and find the function H(x,y): { x′= 2y + x^2+ 1, y′= −2xy +…

Q: If y = 2² is one solution of x²y" + 2xy' − 6y = 0, find the other linearly independent solution.

Q: Find a general solution of the given equation. Do not use the matrix exponential method. 1 2 [83] 0…

Q: x' = x+2y x(0)=1, y(0)=2 y' = 2x+ 4y

Q: There are three interconnected tanks, each with volume 10 liters and containing saline solution.…

Q: -4 2 dx dt -10 4 3 with x(0) = 3 Give your solution in real form. X1 = X2 = An ellipse with…

Q: 3 9 dx dt -1 -3 2 and x(0) 4 ||

A: In the question it is provided a system of differential equations:

Q: Q (3). In a dynamical system, given a system of linear differential equations as: x;'= 3x; +3x, - 6e…

Q: A tank contains 175 liters of fluid in which 20 grams of salt is dissolved. Brine containing 0.75…

A: Given: A tank contains 175 liters of fluid. Amount of Salt in the fluid = 20 grams Brine containing…

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

Q: S. The transfer function of a system is given by Y(s) Gs) = 6. X(s)+ 5+2 Find the differential…

Q: For the system, 6 -1 Y' = Y 5 4 Write the natural period of the oscillations, round the answer to…

Q: Find a particular solution of the linear system given. x'=3x-y y'=5x-3y where x(0) = 1, y(0) = -1

A: Given system of equation is., x' = 3x - yy' = 5x - 3y where x(0) = 1; y(0) = -1 First we find the…

Q: Find the general solution of the following system: 1 1 sint x' 4 1

Q: For each system of differential equations, sketch the lines in the direction of the genvectors .…

A: Find the eigen values and the corresponding eigenvectors of each system. Then draw the phase…

Question

You are given the following inhomogeneous system of first-order differential
equations for x(t) and y(t) in matrix form:

x ̇ = 2 x + y + 3 e ^t,
y ̇ = 4 x − y .

Write down the complementary function for the system of equations and then find a particular integral for the original inhomogeneous system. Please explain each step

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step by step

Solved in 7 steps with 7 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. dx/dt = 2x - 3y and dy/dt = 3x + 2y. THEN, eliminate x and solve the remaining differential equation for y.
Q6.2 [8] Solve the following linear system of differential equations using diagonalization. da dt dx2 = 2+3+1 = 2x+2-1 dt
Suppose that the characteristic equation of a homogeneous constant coefficient linear equation is given by (A2 – 62 + 10)²(A – 1)2 = 0. Find the order of the equation, but not the actual equation.
Find the general solution of the fourth order linear equation y(4) + 4y" + 4y = 0.
Consider the general first-order linear equation y'(t) + a(t)y(t) = f(t). This equation can be solved by defining the integrating factor p(t) = e a(t) dt and then multiplying both sides of the equation by p. The equation becomes p(t) (y'(t) + a(t)y(t)) = (P(t)y(t)) = p(t)f(t). To obtain the solution, d %3D integrate both sides with respect to t. Use this method to solve the following. Begin by computing the integrating factor. 3 y'(t) + y(t) = 5- 6t, y(2) = 0 What is the integrating factor? p(t) = What is the solution? y(t) = where t>0
Use the finite difference method to solve the system of equation given by: y"+ 2y" + y' +y = x² y(0) = 0.2, y(1) = 0.8, & y(2) = 0.2
please provide a clear hand-written solution
Convert the Second order ODE x''+2x'+9x+5=0 to a first order system of two equations. Use y for x'. x'(t) = ? y'(t)= ?
Which of the following are first-order linear equations? y +x?y = 1 xy +y = e (b) y' +xy2 = 1 (d) xy + y = ey
5. Okay, time for some mathematics. We're going to focus on the interactions between the hares and their main predators, the lynx. The tool we need is differential equations (last seen when we talked about the S-I-R disease model). We will let H(t) be the density of hares at time t, and L(t) the density of lynx at time t. Our first assumption is that, if there are no lynx around, the hares grow exponentially. Hares lead to more hares and faster growth. This gives us the differential equation (trust me): HP = aH dt where a is a positive constant. Second we assume that, if there are no hares around, the lynx starve and thus their numbers decay exponentially. This gives us: TP = -bL dt
Convert the following equation to the form of a Sturm-Louville equation3x^2 y´´ (x) + 4xy´ + 6y(x) + λy(x) =0 , x>0