[All Steps] The equation y^prime \prime-2 x y^prime+2 α y=0, where α is a constant, is called the Hermite equation. Find two linearly independent

Question: The equation

\[y^{\prime \prime}-2 x y^{\prime}+2 \alpha y=0,\]

where $\alpha$ is a constant, is called the Hermite equation.

Find two linearly independent solutions on \(-\infty
Show thạt there is a polynomial solution of degree $n$, for the case when $\alpha=n$ is a non-negative integer.

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Solution: The downloadable solution consists of 2 pages
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[All Steps] The equation y^prime \prime-2 x y^prime+2 α y=0, where α is a constant, is called the Hermite equation. Find two linearly independent

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