1. 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.)   The method to obtain the solution is straightforward.

Let's say 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?  2. Originally Posted by iopst How do we obtain these two different solutions from one straightforward method?
Remember that this is a differential equation; choosing different values for k gives you completely different equations with completely different solutions, as you have demonstrated with your example. This isn't really surprising.  3. Originally Posted by Markus Hanke Remember that this is a differential equation; choosing different values for k gives you completely different equations with completely different solutions, as you have demonstrated with your example. This isn't really surprising.
I wasn't surprised, just puzzled.

How does it all work out mathematically? In terms of getting two different solutions.  4. Originally Posted by iopst I wasn't surprised, just puzzled.

How does it all work out mathematically? In terms of getting two different solutions.
I am not really sure what you are asking. The presence or absence of the minus sign makes this two completely different equations, hence you get two completely different solutions. Differential equations do not behave the same way as algebraic equations.  5. Originally Posted by Markus Hanke I am not really sure what you are asking. The presence or absence of the minus sign makes this two completely different equations, hence you get two completely different solutions. Differential equations do not behave the same way as algebraic equations.
Nevermind I've figured it out.  Posting Permissions
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