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Differential Equations question

2022 · 24 Jun · Shift 1 · Q32

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JEE Main
Mathematics
Differential Equations
2022 · 24 Jun · Shift 1 · Q32

Differential Equations question

2022 · 24 Jun · Shift 1 · Q32

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

If x = x(y) is the solution of the differential equation

y{{dx} \over {dy}} = 2x + {y^3}(y + 1){e^y},\,x(1) = 0

; then x(e) is equal to :

A
${e^3}({e^e} - 1)$
B
${e^e}({e^3} - 1)$
C
${e^2}({e^e} + 1)$
D
${e^e}({e^2} - 1)$

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