Infinite differential equation

Calculus Level 4

\[ \large y = \sum_{n=1}^\infty \dfrac{d^n y}{dx^n} \]

If the general solution to the differential equation above can be expressed as

\[ \alpha (\sin x - \cos x) + Ce^{ \beta x}. \]

Find the value of \( \alpha + \beta\).

Note: \(C\) is an integration constant.

Clarification: \( \dfrac{d^n y}{dx^n} \) denotes the \(n^\text{th} \) derivative of \(y\) with respect to \(x\).

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