- #1

astropi

- 47

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**question concerning basic Diff.Eq. 2nd order "trick"**

## Homework Statement

First of all, this is NOT for homework. In fact, this is a conceptual question. Now then, let me address my problem by presenting a simple example. Lets say you have a second order equation with initial conditions:

y(-1) = 2 & y'(-1) = 1

You can solve the D.E. by just applying the boundary conditions as usual, but I also understand there is a "trick". The trick is to rewrite the general solution. In other words, you can solve it the normal way by applying your ICs on (note the actual equation does not matter):

y = c_1e^{r_1t} + c_2e^{r_2t}

or you can use this "trick"

y = d_1e^{r_1(t+1)} + d_2e^{r_2(t+1)}

honestly, I don't remember where this trick comes from. It's supposed to simplify the equation, because then when you apply -1 to t your exponents go to 0. However, could someone explain WHY this is valid? When exactly can you use this, and when can you not? Thanks, hopefully I've been clear about this.

-astropi

ps I tried to use [tex] and the thing totally messed up! What's up with that?