Question

If $y=e^{(k+1)x}$ is a solution of differential equation $\frac{d^{2}y}{d{x}^2}-4\frac{dy}{dx}+4y=0$, then k__.

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

Answer: (C)

$1$

$y=e^{(k+1)x}\Rightarrow y^{\prime }=(k+1)e^{(k+1)x}\Rightarrow y^{\prime \prime }={(k+1)}^2{e}^{(k+1)x}=(k^2+2k+1)e^{(k+1)x}\Rightarrow y^{\prime \prime }-4y^{\prime }+4y=\mathrm{0.....}\left(2\right)$

Putting the values of $y$, $y^{\prime }$ and $y^{\prime \prime }$ in equation (2) we get
$k=1$