# Homework Help: General Solution to ODE

1. Nov 8, 2009

### SpartanG345

1. The problem statement, all variables and given/known data
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

2. Relevant equations

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

3. 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

2. Nov 8, 2009

### 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?

3. Nov 8, 2009

### Staff: Mentor

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.

4. Nov 8, 2009

### SpartanG345

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

5. Nov 8, 2009

### SpartanG345

are u saying C is all real numbers except 0?

6. Nov 8, 2009

### 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?

7. Nov 8, 2009

### Staff: Mentor

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