Question

The number of solutions of `("d"y)/("d"x) = (y + 1)/(x - 1)` when y (1) = 2 is ______. 

पर्याय

• None

• One

• Two

• Infinite

Answer 1

The number of solutions of `("d"y)/("d"x) = (y + 1)/(x - 1)` when y (1) = 2 is one. 

Explanation:

The given differential equation is `("d"y)/("d"x) = (y + 1)/(x - 1)`

⇒ `("d"y)/(y + 1) = ("d"x)/(x - 1)`

Integrating both sides, we get

`int ("d"y)/(y + 1) = int ("d"x)/(x - 1)`

⇒ log(y + 1) = log(x – 1) + log c

⇒ log(y + 1) – log(x – 1) = log c

⇒ `log|(y + 1)/(x - 1)|` = log c

⇒ `(y + 1)/(x - 1)` = c

Put x = 1 and y = 2

⇒ `(2 + 1)/(1 - 1)` = c

∴ c = `oo`

∴ `(y +1)/(x - 1) = 1/0`

⇒ x – 1 = 0

⇒ x = 1.