Here is what I'm looking at:
Use the method of reduction of order to find a second solution to
Here is what I did:
Now, when I plug the original ODE into a solver, the general solution comes up with this:
Does that mean that my solution to is wrong? And if so, where did I make a mistake?
It's like how if you have , etc... you can take all of those cases and just revert it back to being a simple +c. But as soon as it's attached to a variable, such as cx, you can't revert that back to a simple c.
If we were looking at:
...then this could be rewritten as
...in which case, I can see the two constants being merged. But with what we actually have, seperating out the k would leave it still attached to a variable. And I don't understand how we can merge it with the other constant while it's in that state.