Question

The curve passing through (0, 1) and satisfying `sin(dy/dx) = 1/2` is ______.

Options

• `cos((y + 1)/x) = 1/2`

• `sin((y - 1)/x) = 1/2`

• `cos(x/(y + 1)) = 1/2`

• `sin(x/(y - 1)) = 1/2`

Answer 1

The curve passing through (0, 1) and satisfying `sin(dy/dx) = 1/2` is `underlinebb(sin((y - 1)/x) = 1/2)`.

Explanation:

We have `sin(dy/dx) = 1/2`

⇒ `(dy)/(dx) = π/6`

⇒ y = `π/6x + c`

∴ The curve passes through (0, 1) ⇒ C = 1

∴ y = `π/6x + 1` ⇒ `(y - 1)/x = π/2` = `sin^-1  1/2`

⇒ `sin((y - 1)/x) = 1/2`