Find the general solution to the given system of differential equations. Then find the specific solution that

Question:

Find the general solution to the given system of differential equations. Then find the specific solution that satisfies the initial conditions. (Consider all functions to be functions of t.)

x′ = x + 3z, x(0) = 2

y′ = x - 2y + z, y(0) = 3
z′ = 3x + z, z(0) = 4

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra A Modern Introduction

ISBN: 978-0538735452

3rd edition

Authors: David Poole

See More Books

Question Posted: Nov 13, 2018 09:03 AM

See More Questions

Find the general solution to f + f = 2.
Find the general solution to the following complex ordinary differential equations. Verify that, in these cases, the real and imaginary parts of a complex solution are not real solutions. (a) u' + iu...
Find the general solution to the following systems. Distinguish between the vibrational and unstable modes. What constraints on the initial conditions ensure that the unstable modes are not excited?...
A problem in Statistics is given to three students A, B, and C whose chances of solving it are 1/4 and 1/5 respectively. Find the probability that the problem will be solved if they all try...
How would each of these events affect the supply or demand for Japanese yen? 1. Stronger U.S. economic growth. 2. A decline in Japanese interest rates. 3. Higher inflation in the United States.
Write the structure obtained when electrons move as indicated by the curved arrows in the following structure: Does each atom in the resulting structure have a complete valence shell of electrons?...
Exercise 2.143 introduces a study examining the relationship between football playing and hippocampal volume, in $\mu \mathrm{L}$, in the brain. We use the $n=25$ participants in the control...
During the current year, Garrison Construction trades an old crane that has a book value of $80,000 (original cost $140,000 less accumulated depreciation $60,000) for a new crane from Keillor...
Solve the Linear Systems by the method of elimination using Gaussian elimination for matrix linear algebra. linear equation 1 ( 2 x + 4 y + 6 z = - 1 2 ) Linear equation 2 ( 2 x - 3 y - 4 z = 1 5 )...
Compare a companys strategic plan with a football teams game plan.
Find the general solution to the given system of differential equations. Then find the specific solution that satisfies the initial conditions. (Consider all functions to be functions of t.) y 1 = y...
A scientist places two strains of bacteria, X and Y, in a petri dish. Initially, there are 400 of X and 500 of Y. The two bacteria compete for food and space but do not feed on each other. If x =...
Explain why melting ice caps cause Earths temperature to rise. (Hint: Use the term albedo.)
An impulse of 2 . 1 N s directed south is imparted on a tennis ball with mass 6 0 g . If the ball had a velocity of 1 5 m / s north before contact, what is the velocity of the ball after contact ?
1. A child attaches a 1 5 . 5 cm string to a 2 5 g ball and begins twirling it around his head. He twirl it faster and faster. If the string can withstand 9 5 newtons of force before it breaks, how...
Red blood cells can often be charged. Consider two red blood cells with the following charges: 1 6 . 6 pCand + 4 8 . 6 pC . The red blood cells are 3 . 7 0 cm apart. What is the magnitude of the...
In scenario A, the formula to calculate the future value after 20 years is indeed Ct = PV (1 + r)20. This formula considers 20 compounding periods because the interest is applied annually. Each year,...
A partnership has the following capital balances: Germanese, Capital $640,000 Arent, Capital $250,000 Vertus, Capital $115,000 Profits and losses are currently split 10:7:3 Ryan invests $300,000 to...
How does training differ from education? Which of the two is offered to a larger audience with regard to InfoSec?
A copper rod of length L =18.0 in is to be twisted by torques T (see figure) until the angle of rotation between the ends of the rod is 3.08. (a) If the allowable shear strain in the copper is 0.0006...
What is the standard error of d ? Suppose we decide a better measure of the effectiveness of the drug is the mean decrease in blood pressure rather than the measure of effectiveness used previously....
What is a 95% CI for the population mean of d? Suppose we decide a better measure of the effectiveness of the drug is the mean decrease in blood pressure rather than the measure of effectiveness used...
Can we make a statement about the effectiveness of the drug? Suppose we decide a better measure of the effectiveness of the drug is the mean decrease in blood pressure rather than the measure of...
Describe the value chain analysis methods that a firm might utilize to identify strategies to enhance organizational capabilities.
Nurses are advocates for patients and must find a balance while delivering patient care. Discuss
The geriatric nurse cares for patients who are aging or suffering from conditions normally, Discuss?

Find the general solution to the given system of differential equations. Then find the specific solution that

Question:

Step by Step Answer:

The coefficient matrix is which has eigenvalues 1 4 ...View the full answer

Linear Algebra A Modern Introduction

Students also viewed these Mathematics questions