Question

The particular solution of the differential equation log `("dy"/"dx")` = x, when x = 0, y = 1 is ______.

विकल्प

• y = e^x + 2

• y = - e^x 

• y = - e^x + 2

• y = e^x 

Answer 1

The particular solution of the differential equation log `("dy"/"dx")` = x, when x = 0, y = 1 is y = e^x .

Explanation:

We have, differential equations,

log `("dy"/"dx") = x => "dy"/"dx" = "e"^x`

⇒ dy = e^x dx

Integrating on both sides, we get

∫ dy = ∫ e^x dx

⇒ y = e^x + C      ...(i)

On putting x = 0, y = 1 is Eq. (i), we get

1 = e⁰ + C ⇒ C = 0

Now, particular solution of the given differential is y = e^x.