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Hey all,

I have an exam coming up and the pattern of questions seems to include some that I am stumped with.

One goes like this:

The second order differential equation

has non-constant coefficients. Find the general solution by looking for a solution y = x

I would love to say "this is what I have done" but I just couldn't see anything. I tried substituting y = x

Cheers,

The Bob (2004 ©)

I have an exam coming up and the pattern of questions seems to include some that I am stumped with.

One goes like this:

The second order differential equation

x

^{2}y'' - 6xy' + 12y = 0,has non-constant coefficients. Find the general solution by looking for a solution y = x

^{n}and finding a quadratic equation for n.I would love to say "this is what I have done" but I just couldn't see anything. I tried substituting y = x

^{n}, y' = nx^{n-1}and y'' = n(n-1)x^{n-2}into the equation but that just doesn't help, so far as I can see. I need a nudge in the right direction.Cheers,

The Bob (2004 ©)

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