Question

The general solution of the system of coupled equations d x d t = 2 x...

The general solution of the system of coupled equations d x d t = 2 x + a y , d y d t = b x + c y can be written as

[ x ( t ) y ( t ) ] = C 1 [ − 1 1 ] e t + C 2 [ 2 2 ] e 3 t. Determine the values of a =  , b =  , c =  . Give the values of C 1 =  and C 2 =  (as a decimal) if x ( 0 ) = y ( 0 ) = 1.

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
solve the following system of differential equations and find the general solution (D+3)x+(D-1)y=0 and 2x+(D-3)y=0 please...
solve the following system of differential equations and find the general solution (D+3)x+(D-1)y=0 and 2x+(D-3)y=0 please show the steps
Solve the following system of equations and select the correct general solution from below. x’ =...
Solve the following system of equations and select the correct general solution from below. x’ = -2y and y’ = (1/2) x   
Find the (real-valued) general solution to the system of ODEs given by: X’=[{-1,-1},{2,-3}]X (X is a...
Find the (real-valued) general solution to the system of ODEs given by: X’=[{-1,-1},{2,-3}]X (X is a vector) -1,-1, is the 1st row of the matrix 2,-3, is the  2nd row of the matrix. Then, determine whether the equilibrium solution x1(t) = 0, x2(t) = 0 is stable, a saddle, or unstable.
Question 11: What is the general solution of the following homogeneous second-order differential equation? d^2y/dx^2 +...
Question 11: What is the general solution of the following homogeneous second-order differential equation? d^2y/dx^2 + 10 dy/dx + 25.y =0 (a) y = e 12.5.x (Ax + B) (b) y = e -5.x (Ax + B) (c) y = e -10.x (Ax + B) (d) y = e +5.x (Ax + B) Question 12: What is the general solution of the following homogeneous second-order differential equation? Non-integers are expressed to one decimal place. d^2y/dx^2 − 38.y =0 (a) y...
Find a general solution to the system X' = A X(t) for the given matrix A...
Find a general solution to the system X' = A X(t) for the given matrix A -3 5 -2 3
A system of differential equations having the form t(~x)' = A ~x, where A is a...
A system of differential equations having the form t(~x)' = A ~x, where A is a matrix with constant entries, is known as a Cauchy-Euler system. (a) Suppose λ is an eigenvalue of A and ~ v is an eigenvector corresponding to λ. Show that the function x(t) = t^λ (v) is a solution to the Cauchy-Euler system t(x)' = A(x). (b) Solve the following Cauchy-Euler system: t(x)' = 3 -2 2 -2 (x) (t > 0)
First, create 3 equations of the form ax+by+cz=d , where a, b, c, and d are...
First, create 3 equations of the form ax+by+cz=d , where a, b, c, and d are constants (integers between – 5 and 5). For example, x + 2y – 2= -1 . Perform row operations on your system to obtain a row-echelon form and the solution. Go to the 3D calculator website GeoGebra: www.geogebra.org/3d?lang=pt and enter each of the equations. After you have completed this first task, choose one of the following to complete your discussion post. 1. Reflect on...
Find the solution to the linear system of differential equations {x′ = 6x + 4y {y′=−2x...
Find the solution to the linear system of differential equations {x′ = 6x + 4y {y′=−2x satisfying the initial conditions x(0)=−5 and y(0)=−4. x(t) = _____ y(t) = _____
Solve the following differential equations 1. cos(t)y' - sin(t)y = t^2 2. y' - 2ty =...
Solve the following differential equations 1. cos(t)y' - sin(t)y = t^2 2. y' - 2ty = t Solve the ODE 3. ty' - y = t^3 e^(3t), for t > 0 Compare the number of solutions of the following three initial value problems for the previous ODE 4. (i) y(1) = 1 (ii) y(0) = 1 (iii) y(0) = 0 Solve the IVP, and find the interval of validity of the solution 5. y' + (cot x)y = 5e^(cos x),...
This is a differential equations problem: use variation of parameters to find the general solution to...
This is a differential equations problem: use variation of parameters to find the general solution to the differential equation given that y_1 and y_2 are linearly independent solutions to the corresponding homogeneous equation for t>0. ty"-(t+1)y'+y=18t^3 ,y_1=e^t ,y_2=(t+1) it said the answer to this was C_1e^t + C_2(t+1) - 18t^2(3/2+1/2t) I don't understand how to get this answer at all
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT