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tade

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**2nd Order ODE "Contradiction"?**

To solve a 2nd order ODE, we can follow the steps as shown below. (Image 2 is a continuation from Image 1, apologies for the size difference.)

[Broken]

The method to obtain the solution is straightforward.

Let's say

[tex]\frac{d^2y}{dx^2}=ky[/tex]

If k = -1, a possible solution is y = sin x. If k = 1, a possible solution is y = e^x.

How do we obtain these two different solutions from one straightforward method?

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