Question

Find a second-order linear homogeneous equation having the pair as a fundamental set of solutions. Is it correct to say that P(x) = -2x? I found that by taking the derivative of the Wronskian. How do I put together the rest of the differential equation? http://i44.tinypic.com/2qdmtd2.jpg

Answer 1

y=x
y'=1
y''=0

y = x^2
y' = 2x
y'' = 2

f(x)y'' + g(x)y' + h(x)y = 0 i believe would cover the bases

Answer 2

or, since the solution is also defined for any linear combonation of the results:

y = x^2 + x; might be doable

y' = 2x + 1

y'' = 2

hmmm

2 + (2x-1) + (x^2+x) = 0

2 + 2x - 1 + x^2 +x = 0


itll can be some rewriting of this

Answer 3

without the typo of course:

2(x^2/2) - 2xx- 1x + x^2+x = 0

\[\frac{1}{2}x^2y''-xy'+y=0\]

http://www.wolframalpha.com/input/?i=x%5E2y%27%27%2F2-xy%27%2By%3D0

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