General Solution to ODE Quiz Problem: Find n and C for y=Cx^n as a Solution

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Homework Help Overview

The discussion centers around a quiz problem involving the differential equation xdy/dx - 6y = 0, where participants are tasked with finding the values of n and C in the expression y = Cx^n that satisfy the equation.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore substituting y = Cx^n into the differential equation to analyze the conditions under which the equation holds true. There are questions regarding the validity of C being zero and the implications of this choice on the solution.

Discussion Status

Some participants have reached a conclusion that n = 6 and C can be any real number, while others express confusion about the validity of C being zero. The discussion reflects differing interpretations of the problem and the conditions for C.

Contextual Notes

There is mention of a quiz context and the impact of marking on participants' understanding, particularly regarding the acceptance of C as zero. The urgency of an upcoming exam adds to the pressure of clarifying these concepts.

SpartanG345
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Homework Statement


This was a quiz problem
Give the value of n and C for which y=Cx^n is a solution of the equation
xdy/dx - 6y = 0

Homework Equations



ans
n= 6
C= 0 (some triangle symbol) an n .. ineligible mark

The Attempt at a Solution


n = 6
C = All real numbers
my tutor explained it ages ago, but now i am in stuvac i fogot why C isn't all real RE
i have my exam tomorrow and i am just going through mistakes i have made in quizzes
 
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Try and do it yourself. Put y=Cx^n into the left side of the ODE. How can the result be 0 for all x?
 
This is not very complicated. Your differential equation is
xy' = 6y and your solution is y = Cxn

From your solution, y' = nCxn - 1, so xy' = nCxn
From the differential equation, xy' = 6y, so nCxn = 6Cxn, so n = 6 and C can be any real number.
 
oh great lol that's what i got n=6 and C is all RE and i got marked down...tat was 15% quiz...
 
are u saying C is all real numbers except 0?
 
hmm i still don't understand why C can't be zero if it is the solutions is only satisfied when y = 0 and x can be anything...

was my tutor wrong to mark me down?
 
SpartanG345 said:
are u saying C is all real numbers except 0?
No, he is not. You were saying that in your first post.
SpartanG345 said:
ans
n= 6
C= 0 (some triangle symbol) an n .. ineligible mark
 

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