# Relearning differential equations, please help

## Homework Statement

I was never great in diffEQ, but now I have to solve this problem for physics homework and I'm pretty lost.

d^4x/dx^4 - d^2x/dx^2 + a =0

Where a is a parameter.

## The Attempt at a Solution

I have tried solutions like e^kt which work accept for the parameter a. The problem asks specifically what happens if a varies, so I cant even treat it like a constant

Ray Vickson
Science Advisor
Homework Helper
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## Homework Statement

I was never great in diffEQ, but now I have to solve this problem for physics homework and I'm pretty lost.

d^4x/dx^4 - d^2x/dx^2 + a =0

Where a is a parameter.

## The Attempt at a Solution

I have tried solutions like e^kt which work accept for the parameter a. The problem asks specifically what happens if a varies, so I cant even treat it like a constant

I assume you mean ##d^4 x/dt^4##, etc; otherwise your DE makes no sense at all!

I suspect they mean that ##a## is a "parameter" that is fixed throughout a solution, but that different values of ##a## can give you different solutions. At least, that is how I read it. Otherwise, the problem should have written ##a(t)## instead of just plain ##a##.

Anyway, if ##a## really is a constant, the function ##y = d^2 x/dt^2## satisfies ##d^2 y /dt^2 - y + a = 0##, so ##z = y-a## satisfies ##d^2 z /dt^2 - z = 0.##

Yes, there are t's in the denominator. Tha ks so much, I think that will work!