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Differential Equations question

2022 · 29 Jun · Shift 2 · Q36

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JEE Main
Mathematics
Differential Equations
2022 · 29 Jun · Shift 2 · Q36

Differential Equations question

2022 · 29 Jun · Shift 2 · Q36

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

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

\underline{\hspace{2cm}}

.

Numerical answer

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