Let y = y(x), x > 1, be the solution of the differential equation (x - 1)dy/dx + 2xy = 1/(x - 1), with y(2) = (1 + e⁴)/(2e⁴). If y(3) = (e^α + 1)/(β e^α), then the value of α + β is equal to _ _ _ _ _.

Differential Equations: JEE Main 2022 Mathematics question

JEE Main 2022 · 29 Jun, Evening shift · Q33

JEE Main 202229 Jun, Evening shiftMathematicsMediumDifferential Equations163× since 2002

Let y = y(x), x > 1, be the solution of the differential equation

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

, with

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

. If

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

, then the value of

\alpha + \beta

is equal to _________.

Your answerType your answer. Integers and decimals are accepted.