Question

For the differential equation $\frac{dy}{dt}+5y=0$ with y(0) = 1, the general solution is

• A. $e^{5t}$
• B. $e^{-5t}$
• C. $5e^{-5t}$
• D. $e^{\sqrt{-5t}}$

Answer 1

The correct option is B $e^{-5t}$

$\frac{dy}{dt}+5y=0$ ....(i)

$\Rightarrow \frac{dy}{y}=-5dt$
Using variable seperable method

$\Rightarrow logy=-5t+logc$

$\Rightarrow log\left(\frac{y}{c}\right)=-5t$

$\Rightarrow y=c{e}^{-5t}$ ...(ii)

Using y(0) = 1, we get c = 1

$\therefore$ The solution is y = $e^{-5t}$