Question

If `(dy)/(dx)` = y + 3 > 0 and y = (0) = 2, then y (in 2) is equal to ______.

Options

• 5

• 13

• – 2

• 7

Answer 1

If `(dy)/(dx)` = y + 3 > 0 and y = (0) = 2, then y (in 2) is equal to 7.

Explanation:

`(dy)/(dx)` = y + 3

`\implies int (dy)/(y + 3) = int dx`

`implies` ℓ n |y + 3| = x + c

Given y (0) = 2, ∴ ℓ n 5 = c

`\implies` ℓ n |y + 3| = x + ℓ n 5

Put x = ℓn 2, then ℓn |y + 3| = ℓn 2 + ℓn5

`\implies` ℓn |y + 3| = ℓn 10

∴ y + 3 = ± 10 `\implies` y = 7, – 13