Deriving y & Solving y'' + 4y' - 5y = 0 with C

  • Thread starter Thread starter Dr Game
  • Start date Start date
Click For Summary

Homework Help Overview

The discussion revolves around deriving the function y = C e^(-5x) and substituting it into the differential equation y'' + 4y' - 5y = 0. The subject area pertains to differential equations and their solutions.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to understand how the constant C affects the derivatives of the function and its substitution into the differential equation. Some participants discuss the differentiation process while keeping C in the expression.

Discussion Status

The discussion appears to be progressing with participants confirming the differentiation approach and the implications of including the constant C. There is an acknowledgment of the expected outcome when C is included.

Contextual Notes

Participants are considering the implications of the constant C in the context of the differential equation, and there is a focus on the differentiation process without reaching a final resolution.

Dr Game
Messages
26
Reaction score
0
It's been a while, but how would you go about deriving

y = C e^-^5^x

and plug it into this equation

y'' + 4y' - 5y = 0

i can do this without C the answer would be 0, but what do I do with C there?
 
Physics news on Phys.org
You just differentiate it as usual, leaving the C in front of the terms, and then plug the first and second derivatives into the equation.
 
alright thought so, so I should get the same answer if C wasn't there, which is 0

25Ce^-^5^x+4(-5Ce^-^5^x)-5Ce^-^5^x = 0
 
Yes, that's correct
 

Similar threads

Replies
7
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
5
Views
2K