Let y = y(x) be the solution of the differential equation ((x + 2)e^(((y + 1)/(x + 2))) + (y + 1))dx = (x + 2)dy, y(1) = 1. If the domain of y = y(x) is an open interval (α, β), then | α + β | is equal to _ _ _ _ _ _ _.

Differential Equations: JEE Main 2021 Mathematics question

JEE Main 2021 · 22 Jul, Evening shift · Q33

JEE Main 202122 Jul, Evening shiftMathematicsMediumDifferential Equations163× since 2002

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

\left( {(x + 2){e^{\left( {{{y + 1} \over {x + 2}}} \right)}} + (y + 1)} \right)dx = (x + 2)dy

, y(1) = 1. If the domain of y = y(x) is an open interval (

\alpha

\beta

), then |

\alpha

\beta

| is equal to ______________.

Your answerType your answer. Integers and decimals are accepted.