Question

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

पर्याय

• 7 

• 5

• 13

• -2

Answer 1

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

Explanation:

`dy/dx = y + 3`

⇒ `dy/(y + 3) = dx`

Integrating on both sides, we get

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

⇒ log(y + 3) = x + c ......(i)

Since y(0) = 2, i.e., y = 2 when x = 0

∴ log (2 + 3) = 0 + c ⇒ c = log 5

∴ log(y + 3) = x + log 5 .........[From (i)]

⇒ y + 3 = 5e^x

⇒ y = 5e^x - 3 

∴ y(log 2) = `5e^{log2} - 3 = 10 - 3`

= 7