Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Find the values of the constants C and L such that the function y(x) = Cel satisfies to ODE y + y =y".

Find the values of the constants C and L such that the function y(x) = Cel satisfies to ODE y + y =y".

Advanced Engineering Mathematics
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
icon
Related questions
Question
**Problem Statement:** Find the values of the constants \( C \) and \( L \) such that the function \( y(x) = Ce^{Lx} \) satisfies the ordinary differential equation (ODE) \( y + y' = y'' \). **Options:** - \( \circ \) Only two solutions with \( L = \frac{1 \pm \sqrt{5}}{2} \) and \( C = 1 \). - \( \circ \) Two possible solutions with \( L = \frac{1 - i\sqrt{5}}{2} \) and with \( L = \frac{1 + i\sqrt{5}}{2} \). - \( \circ \) Two possible solutions with \( L = \frac{1 - \sqrt{5}}{2} \) and with \( L = \frac{1 + \sqrt{5}}{2} \), and \( C \) can be arbitrary. - \( \circ \) Only one solution with \( L = \frac{1 - \sqrt{5}}{2} \) and \( C \) can be arbitrary.
Transcribed Image Text:**Problem Statement:** Find the values of the constants \( C \) and \( L \) such that the function \( y(x) = Ce^{Lx} \) satisfies the ordinary differential equation (ODE) \( y + y' = y'' \). **Options:** - \( \circ \) Only two solutions with \( L = \frac{1 \pm \sqrt{5}}{2} \) and \( C = 1 \). - \( \circ \) Two possible solutions with \( L = \frac{1 - i\sqrt{5}}{2} \) and with \( L = \frac{1 + i\sqrt{5}}{2} \). - \( \circ \) Two possible solutions with \( L = \frac{1 - \sqrt{5}}{2} \) and with \( L = \frac{1 + \sqrt{5}}{2} \), and \( C \) can be arbitrary. - \( \circ \) Only one solution with \( L = \frac{1 - \sqrt{5}}{2} \) and \( C \) can be arbitrary.
Expert Solution
Step 1: Solution

Given differential equation: y plus y apostrophe equals y apostrophe apostrophe

We have to find the value of constant C and L such that the function y left parenthesis x right parenthesis equals C e to the power of L x end exponent satisfies to ODE 

y plus y apostrophe equals y apostrophe apostrophe

steps

Step by step

Solved in 5 steps with 27 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS