Question: Consider the differential equationy'' y'30y =0.Verify that the functions e5x and e6x form a fundamental set of solutions of the differential equation on the interval

Consider the differential equationy'' y'30y =0.Verify that the functions e5x and e6x form a fundamental set of solutions of the differential equation on the interval (, ).The functions satisfy the differential equation and are linearly independent since the WronskianWe5x, e6x= 0 for < x < .Form the general solution.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Consider the differential equationx2y''+ xy'+ y =0;cos(ln(x)), sin(ln(x)),(0, ).Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated...

y' = ky , to = 0, k has n linearly independent eigenvector insing notation of Section 7.7 in the text D. using a careful proof in a couple of steps to show that P ( t) = I (t) T 10) , and then show...

7. [-/2 Points] DETAILS ZILLDIFFEQMODAP10 4.1.023. 1. [-/2 Points] DETAILS ZILLDIFFEQMODAP10 4.1.001. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider...

Consider the differential equation y ' ' - y ' - 6 y = 0 Verify that the functions e - 2 x and e 3 x form a fundamental set of solutions of the differential equation on the interval ( - , in ) . The...

Consider the differential equation y" - y' 30y = 0. Verify that the functions e-5x and ex form a fundamental set of solutions of the differential equation on the interval (-00, 00). -5x The functions...

8. [-/2 Points] DETAILS ZILLDIFFEQMODAP11 4.1.023. 0/6 Submissions Used Consider the differential equation " - y' - 20y = 0. Verify that the functions ex and ex form a fundamental set of solutions of...

11. [-/1 Points] | DETAILS I ZILLDIFFEQ94.1.021. l MYNOTES ll PRACTICEANOTHER I Determine whether the given set of functions is linearly independent on the interval (00, oo). f1(x) = 2 + x, f2(x) =...

Can you please help me with number 31. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! 5.7 Matrix Exponentials and Linear...

Consider the differential equation y" 2y+ 10y= 0; e* cos(3x), e* sin(3x), (-, ). y"-2y' Verify that the given functions form a fundamental set of solutions of the differential equation on the...

Consider the differential equation x 2 y prime prime 5 x y prime 8 y 0 quad x 2 x 4 0 infty Verify that the given functions form a fundamental set of solutions of the differential equation on the...

The following scores were obtained from a 15-item test in English. Boys: 9, 10, 13, 6, 10,7,9,10,8 Girls: 9,7,5, 12, 3, 8, 10, 2, 8, 10, 14,7 Find the range, absolute deviation, variance, and...

Required: Present the operating activities section of the statement of cash flows for Peak Heights Company using the indirect method. (List cash outflows as negative amounts .) The following...

You contributed to two retirement plans offered by Fidelity and TIAA CREF during your working years. Now, you have reached retirement and plan to consume $ 6 , 0 0 0 per month over the next 2 0...

Monsoon Inc. is considering bidding on a government project. To do the project, the company must make an initial investment of $9 million to purchase the necessary equipment. The project will last...