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Differential Equations

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Difficult

Point at Infinity

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Katie is studying the Euler equation $x^2y''+xy'-4y=0$. She knows that the solution for $x>0$ can be solved by making the substitution $u=\ln x$, but she is interested in the asymptotic behavior of solutions at infinity so this substitution is not very helpful.

For this purpose, she thinks the substitution $\xi=1/x$ is suitable.

By her method, the point at infinity is:

A

an ordinary point.

B

a regular singular point.

C

an irregular singular point.

D

None of the above.