Infinite differential equation

Calculus Level 4

y=n=1dnydxn \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

α(sinxcosx)+Ceβx. \alpha (\sin x - \cos x) + Ce^{ \beta x}.

Find the value of α+β \alpha + \beta.

Note: CC is an integration constant.

Clarification: dnydxn \dfrac{d^n y}{dx^n} denotes the nthn^\text{th} derivative of yy with respect to xx.

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