# 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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