Question

If the characteristic equation of the differential equation $\frac{d^{2}y}{d{x}^2}+2\alpha \frac{dy}{dx}+y=0$ has two equal roots, then the values of $\alpha$ are

• A. $\pm 1$
• B. $0,0$
• C. $\pm j$
• D. $\pm 1/2$

Answer 1

The correct option is A $\pm 1$

$\therefore$ $\frac{d^{2}y}{d{x}^2}+2\alpha \frac{dy}{dx}+y=0$
Characteristic equation is $D^2+2\alpha D+1=0$
For equal roots $B^2-4AC=0$
$\Rightarrow (2\alpha {)}^2-4(1\left)\right(1)=0$
$4{\alpha }^2=4$
${\alpha }^2=1$
$\alpha =\pm 1$