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Differential Equations: JEE Mains 2022 June 29 Shift 2

Hard· Linear differential equations· +4 / 0

Let

y=y(x)

,

x>1

, be the solution of the differential equation

(x-1)\dfrac{dy}{dx}+2xy=\dfrac{1}{x-1}

, with

y(2)=\dfrac{1+e^4}{2e^4}

. If

y(3)=\dfrac{e^\alpha+1}{\beta e^\alpha}

, then the value of

\alpha+\beta

is equal to ______.

Your answer (numerical)

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