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JEE Main20207 Jan 2020Morning ShiftMathematicsDifferential EquationsActual

If y = y x is the solution of the differential equation , e y d y d x - 1 = e x such that y 0 = 0 , then y 1 is equal to

Options

A1 + l o g e 2
B2 + l o g e 2
C2 e
Dl o g e 2

Correct answer

A. 1 + l o g e 2

Step-by-step solution

e y = t e y d y d x = d t d x d t d x - t = e x I F = e - ∫ d x ⇒ t · e - x = x + 1 e y - x = x + 1 y = x + ln ⁡ x + 1 at x = 1 , y = 1 + ln ⁡ 2

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