Trouble with the second root

Original equation: xy'' + y' + 0. I have found that the roots are both 0, and one of the solutions is:

That solution checks. For y2, I tried using , but using P(x) = 1/x, y2 turned into:

which is not even close to the answer in the back of the book. Please advise.

Re: Trouble with the second root

If the equation is:

then I would simply, rewrite the left side as:

separate variables, losing a trivial solution:

Obviously, though, I am missing something...(Thinking)

Re: Trouble with the second root

I mistyped the OP. The differential equation is xy'' + y' + y = 0. (Otherwise, I just set w = y' and solve.)

Everything else is written as intended.

Re: Trouble with the second root

Quote:

Originally Posted by

**phys251** The differential equation is xy'' + y' + y = 0.