Question

Consider the following differential equation:

$\frac{dy}{dx}=-5y;$ initial condition : y = 2 at t = 0

The value of y at t = 3 is

• A. $-5e^{-10}$
• B. $2e^{-10}$
• C. $2e^{-15}$
• D. $-15e^2$

Answer 1

The correct option is C $2e^{-15}$

$\frac{dy}{dt}=-5y$

$\therefore \int \frac{dy}{y}=\int -5dt$

In(y) = -5t + logC

$\Rightarrow y=C{e}^{-5t}$

at t = 0, y = 2

$\therefore$ C = 2

$\therefore$ y at t = 3

$y=e^{-5\times 3}\times 2=2e^{-15}$