If dy/dx = y + 3 > 0 and y(0) = 2 , then y(2) is equal to: - Mathematics MCQ FIITJEE AIEEE 2011 (Set Q) 2026 | ExamTest.live

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If \frac{d y}{d x} = y + 3 > 0 and y (0) = 2, then y (ln 2) is equal to:

Solution & Step-by-step Explanation

\frac{d y}{y + 3} = d x Integrating both sides: ln (y + 3) = x + C At x = 0, y = 2 ⟹ ln (5) = 0 + C ⟹ C = ln 5 .So, ln (y + 3) = x + ln 5 . y + 3 = e^{x + l n 5} = 5 e^{x} .At x = ln 2 : y + 3 = 5 e^{l n 2} = 5 (2) = 10 y = 10 - 3 = 7

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If \frac{d y}{d x} = y + 3 > 0 and y (0) = 2, then y (ln 2) is equal to:

5

13

- 2

7

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