Hi,

Need some help with an assignment question. I think I have it worked out but I am a little rusty with some basic principles

Any help will be greatly appreciated.

Q: Verify that the functions cos(ln x), sin(ln x), form a fundamental set of solutions of the DE x^{2}y′′ + xy′ + y = 0, on the interval (0, ∞). Form the general solution.

My attempt and my confusion:

I have verified that both y1(x)= cos(lnx) and y2(x)= sin(lnx) are solutions of the DE.

I have then tried to verify if W(y1,y2) does not equal 0

w(y1,y2)= cos(lnx)*(cos(lnx)/x) - ((-sin(lnx)/x)*sin(lnx))

= (cos^2(lnx) + sin^2(lnx))/x

= 1/x which does not equal 0

Confusion: The interval is (0, ∞) and x cannot be 0, so does this mean the Wronskian is discontinuous at x? And would it make the equation linearlydependent?

Thanks!

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