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# Homogeneous Linear Equations watch

1. Can anyone check whether I'm solving these algorithmic problems correctly?

1.

are solutions.

is real general solution.

2.

are solutions.

is general solution.

3.

are solutions.

is general solution.
2. Do they work if you substitute y back into your original equation?
3. (Original post by pie_monster)
Do they work if you substitute y back into your original equation?
Yes they do although the first one took a bit of time to check!
4. Your 2nd and 3rd solutions are incomplete. You should expect as many arbitrary constants as the order of the highest derivative. That is, 3 solutions for the 2nd question and 4 solutions for the 3rd.
5. (Original post by DFranklin)
Your 2nd and 3rd solutions are incomplete. You should expect as many arbitrary constants as the order of the highest derivative. That is, 3 solutions for the 2nd question and 4 solutions for the 3rd.
So for the 2nd would you say that is a repeated root and so

?

and for the 3rd, are repeated roots and so

?
6. Yes for the 2nd question, no for the 3rd. (+/-1 are not repeated roots).

And again, I point out to you that if you want to check a solution, the simplest thing to do is differentiate and substitute in. I'm assuming you're at university now, in which case you need to start doing these things for yourself.
7. (Original post by DFranklin)
Yes for the 2nd question, no for the 3rd. (+/-1 are not repeated roots).

And again, I point out to you that if you want to check a solution, the simplest thing to do is differentiate and substitute in. I'm assuming you're at university now, in which case you need to start doing these things for yourself.
There are two more complex roots to the 3rd but the question states find the real general solution.

Do I just discard the complex ones or do something similar to what I did in the 1st one in which case would I add a cosx+sinx to the general solution to make it:

?

I checked it and it works by the way as so when you take them away = 0.

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