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## Homework Statement

Hi,

It's been a while since I have taken differential equations. How do I solve an equation like this:

[itex]k_{1}\frac{d^{2}V_{x}(t)}{dt^{2}}+k_{2}\frac{dV_{x}(t)}{dt}+k_{3}V_{x}(t)=0[/itex]

## Homework Equations

## The Attempt at a Solution

I have looked through my books and it says to assume that

[itex]V_{x}(t) = Ae^{st}[/itex]

The book then goes on to solve the equation which I can follow. However I would like to know how to actually solve the problem mathematically without "assuming". If I remember correctly you can use something called Laplace transforms. However, I don't really remember if you can solve this equation using Laplace transforms. Thanks for any help.