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

Options

A. `y = e^(x) + 2`
B. `y = - e^(x)`
C. `y = - e^(x) + 2`
D. `y = e^(x)`

Answer

D

Explanation

We have, differential equations.
`log ((dy)/(dx)) = x implies (dy)/(dx) = e^(x)`
`implies dy = e^(x) dx`
Integrating on both sides, we get
`int dy = int e^(x) dx`
`implies y = e^(x) + C`
On putting x = 1, is Eq. (i) we get
`1 = e^(0) + C implies C = 0`
Now, particular solution of the given differential is `y = e^(x)`