Independent Solutions Show that if r1 and r2 are distinct real characteristic roots of equation (1), then

Question:

Independent Solutions Show that if r1 and r2 are distinct real characteristic roots of equation (1), then the solutions e'' 1 and er2t are linearly independent?

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

Step by Step Answer:

Related Book For book-img-for-question

Differential Equations and Linear Algebra

ISBN: 978-0131860612

2nd edition

Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West

See More Books

Question Posted: May 26, 2016 06:05 AM

See More Questions

Show that if r1 and r2 are distinct real roots of the auxiliary equation, then y = C1er1x + C2er2x is a solution of y" + a1 y' + a2 y = 0?
Show that if r1 and r2 are distinct real roots of the auxiliary equation, then y = C1er1x + C2er2x is a solution of y" + a1y' + a2 y = 0?
The Euler-Cauchy Equation A well-known linear second-order equation with variable coefficients is the Euler-Cauchy Equation3 Where a, b, c ( IR. and a of; 0. Show by substituting y = tr that...
The following are some transactions of Surendal Company for 2024. Surendal Company uses straight-line depreciation and has a December 31 year end. Apr. 1 Retired a piece of equipment that was...
The Tufte family leased a 260-acre farm from the Travelers Insurance Co. Toward the end of the lease, Travelers mailed the Tuftes an option to renew the lease. The option arrived at the Tuftes house...
When a molecule absorbs a photon, momentum is conserved. If an H 2 molecule at 500. K absorbs an ultraviolet photon of wavelength 175 nm, what is the change in its velocity, v? Given that its average...
Determine the probability mass function of $X$ from the following cumulative distribution function: \[ F(x)=\left\{\begin{array}{lr} 0 & x. \] Figure 3.3 displays a plot of $F(x)$. From the plot,...
Bloom Company management predicts that it will incur fixed costs of $160,000 and earn pretax income of $164,000 in the next period. Its expected contribution margin ratio is 25%. Use this information...
A company achieved annual sales of 1,000 units last year, charging $25 for each unit. It costs the company $10 to produce each unit (average variable cost) whilst fixed cost was $5,000. a) Calculate...
Pagnol-Carrelages SNC is a small distributor of marble tiles. Pagnol-Carrelages identifies its three major activities and cost pools as ordering, receiving and storage, and shipping, and reports the...
Sorting Graphs: For the DE + 5+ 6x = 0 of Example 1, Fig. 4.2.8 adds to Fig. 4.2.1 the linked solution graph for (t). Label the phase-plane trajectories from left to right as A, B, C. D, E. Then...
Second Solution: Verify that if the discriminant of equation (1) as given by ( = b2 - 4ac is zero, so that b2 = 4ac and the characteristic root is r = - b/2a, then substituting y = v(t)e-(b/2a)r into...
Use the rounding rules to round the following. 189.9895 =
AAA Corp. shares will pay next year a dividend of $5.00 and is expected that the dividends will grow at a rate of 4.0% annually forever. It currently has 500,000 common shares outstanding trading at...
Calculate the present value of three payments of $ 8 , 1 8 8 , 1 2 8 . 0 0 , each to be received at the end of the year for the next three years from today, if the rate of interest is equal to 8 % .
Before deciding to deposit her money at the credit union, Heather checked the interest rates at her local bank as well. The bank was paying a nominal interest rate of 9.8% compounded quarterly. If...
You earn $4,000 a month. After taxes, social security contributions, and living expenses you have $600 per month that you can and will save. What is the future value of $600 saved every month for 30...
According to the Tableau article on designing great visualizations, what are the three types of data? Group of answer choices Quantitative Ordinal Interval Nominal
For the following exercises, perform the indicated operation and express the result as a simplified complex number. 4+ V-20 2
Compare and contrast debt financing and equity financing as ways of starting a new business. Does one have an overall advantage over the other? What situation is more favorable to the use of debt...
Find the Laplace transforms of the functions given in Problems 11 through 22. f(t) = cos t if 0 t 2; f(t) = 0 ift > 2
Use Laplace transforms to solve the initial value problems in Problems 1 through 16. x" + 2x + 4y = 0, y" + x + 2y = 0; x (0) = y(0) = 0, x' (0) = y'(0) = -1
Use the transforms in Fig. 10.1.2 to find the Laplace transforms of the functions in Problems 11 through 22. A preliminary integration by parts may be necessary. f (t) = t - 2e 3t t f(t) t" (n 0) g@...
s Machine-hours required to support estimated production Fixed manufacturing overhead cost Variable manufacturing overhead cost per machine-hour Required: 1. Compute the plantwide predetermined...
How do visionary leaders navigate the complexities of organizational dynamics to cultivate a culture of innovation and adaptability ? Explain
Finnish Corporation manufactures custom molds for use in the extrusion industry. The company allocates manufacturing overhead based on machine hours. Selected data for costs incurred for Job 532 are...

Independent Solutions Show that if r1 and r2 are distinct real characteristic roots of equation (1), then

Question:

Step by Step Answer:

Substituting y vte bt2a into ay by cy 0 Gives Substituting v v v ...View the full answer

Differential Equations and Linear Algebra

Students also viewed these Linear Algebra questions