Question

The solution of the differential equation $\frac{dy}{dx}-ky=0,y\left(0\right)=1$ approach zero when $x\to \infty$, if

• A. K = 0
• B. k > 0
• C. k < 0
• D. none of these

Answer 1

The correct option is C k < 0

$\frac{dy}{dx}-ky=0,\frac{dy}{y}=kdx$
In $y=kx+c$
At $x=0,y=1\therefore c=0$
Now, In y = kx
$y=e^{kx}\underset{x\to \infty }{Lim}y=\underset{x\to \infty }{Lim}{e}^{kx}=0\therefore k<0$