Specific solution of diff eq, no initial value

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Homework Help Overview

The discussion revolves around finding specific solutions to a differential equation without initial values. Participants are exploring the nature of solutions, particularly focusing on the form of the solutions and the implications of different values of n.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the general solution of the form y = Cx^3 and question whether alternative forms, such as y = |x|^3, could also be valid solutions. There is also consideration of the trivial solution y = 0 and its relevance to the problem.

Discussion Status

The discussion is active, with participants sharing their thoughts on potential solutions and questioning the wording of the original problem. Some guidance has been offered regarding the nature of solutions, but there is no explicit consensus on the desired form of the second solution.

Contextual Notes

Participants note the absence of initial values and express uncertainty about what specific solutions are being sought, indicating a potential ambiguity in the problem statement.

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Homework Statement


Consider the differential equation
059b0fc5ef0cd85a055fc8a05eef301.png


Find a general solution to this differential equation that has the form
c1403c12bfdafbad58b32041c1e5381.png

.
.
.
y = Cx3

Find a second solution
c1403c12bfdafbad58b32041c1e5381.png
that might not be a general solution and which may have a different value of n than your first solution.

The Attempt at a Solution


I solved the first part of the problem
y = Cx3

But am at a complete loss for how to find a second explicit solution without being given an initial value.
 
Last edited:
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I'm guessing ##y=0## isn't what is being wanted here although it is a solution.

Question: Is ##y = |x|^3## a solution?
 
Why would you guess that? [tex]y= 0x^n[/tex] is a solution for any n.
 
LCKurtz said:
I'm guessing ##y=0## isn't what is being wanted here although it is a solution.

Question: Is ##y = |x|^3## a solution?

HallsofIvy said:
Why would you guess that? [tex]y= 0x^n[/tex] is a solution for any n.

Are you addressing me? Yes, I know it is a solution for any n, as I said. But, given the poor wording of the question, I thought they might be looking for the more interesting ##y = |x|^3##.
 
I've tried y=0 and y=e^c(x^3), I'll see if it accepts y=0x^n but I think they're looking for a specific nedit: 0x^n was it! Thanks!
 

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