Relearning differential equations,

[Daniel Sellers]

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.

Homework Equations

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 can't even treat it like a constant

 

[Ray Vickson]

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.

Homework Equations

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 can't 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 $d^2 z /dt^2 - z = 0.$

 

[Daniel Sellers]

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