Solving the Initial Value Problem for 'y' = x, x' = -5y-4x

Click For Summary

Homework Help Overview

The discussion revolves around solving an initial value problem involving a system of differential equations: y' = x and x' = -5y - 4x, with initial conditions y(0) = 1 and x(0) = 0. Participants are exploring the application of initial values to find a complete solution.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the process of applying initial conditions to a general solution, with one suggesting the need to solve for undetermined coefficients. Others question the interpretation of the variables and the role of the independent variable in the context of the equations.

Discussion Status

The discussion is active, with participants providing guidance on how to apply initial conditions and questioning the assumptions regarding the independent variable. There is no explicit consensus, as differing interpretations of the equations are being explored.

Contextual Notes

Some participants express uncertainty about the treatment of x and y as functions of a variable, as well as the implications of the derivatives represented by primes. This indicates a potential area of confusion regarding the formulation of the problem.

Ry122
Messages
563
Reaction score
2
y' = x
x' = -5y-4x

y(0) = 1
x(0) = 0

after finding the general solution as shown here
http://www.wolframalpha.com/input/?i=y'+=+x,+x'+=+-5y-4x

how do you go about applying the initial values and finding the complete solution?
 
Physics news on Phys.org
Your general solution should have two undetermined coefficients. Substitute 0 for t, set x= 0, y= 1 and you will have two equations to solve for the two coefficients.
 
actually I don't think wolfram alpha has done the correct thing in making x and y a function of t as there's no mention of another variable in the original equations. What would you do when they aren't functions of t?
 
You can call the independent variable whatever you want! What did you mean by x' and y'? I assumed the primes were derivatives. With respect to what variable?
 

Similar threads

Replies
7
Views
2K
  • · Replies 2 ·
Replies
2
Views
5K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 25 ·
Replies
25
Views
2K
Replies
2
Views
2K
Replies
25
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 13 ·
Replies
13
Views
13K
  • · Replies 18 ·
Replies
18
Views
3K