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

[SpartanG345]

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

 

[Dick]

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?

 

[Mark44]

This is not very complicated. Your differential equation is
xy' = 6y and your solution is y = Cxⁿ

From your solution, y' = nCx^{n - 1}, so xy' = nCxⁿ
From the differential equation, xy' = 6y, so nCxⁿ = 6Cxⁿ, so n = 6 and C can be any real number.

 

[SpartanG345]

oh great lol that's what i got n=6 and C is all RE and i got marked down...tat was 15% quiz...

 

[SpartanG345]

are u saying C is all real numbers except 0?

 

[SpartanG345]

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?

 

[Mark44]

are u saying C is all real numbers except 0?

No, he is not. You were saying that in your first post.

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