Question

If y = `sqrt((1 - x)/(1 + x))`, then `(1 - x^2) dy/dx + y` = ______.

Options

• 0

• 1

• –1

• 2

Answer 1

If y = `sqrt((1 - x)/(1 + x))`, then `(1 - x^2) dy/dx + y` = 0.

Explanation:

y = `sqrt((1 - x)/(1 + x))`

∴ log y = `1/2[log(1 - x) - log(1 + x)]`

∴ `1/y dy/dx = 1/2[(-1)/(1 - x) - 1/(1 + x)]`

∴ `1/y dy/dx = 1/2[(-1 - x - 1 + x)/((1 - x)(1 + x))]`

∴ `1/y dy/dx = 1/2[(-2)/(1 - x^2)]`

∴ `(1 - x^2)dy/dx` = – y

∴ `(1 - x^2)dy/dx + y` = 0