GATE ECE 2006 | Question: 27

Question

For the differential equation $\dfrac{d^2 y}{d x^2}+k^2 y=0$, the boundary conditions are

1. $y=0$ for $x=0$, and
2. $y=0$ for $x=a$

The form of non-zero solutions of $y$ (where $m$ varies over all integers) are

• A. $y=\displaystyle{}\sum_m\;\mathrm{~A}_m\;\sin ^{\frac{m \pi x}{a}}$
• B. $y=\displaystyle{}\sum_m\;\mathrm{~A}_m\;\cos ^{\frac{m \pi x}{a}}$
• C. $y=\displaystyle{}\sum_m\;\mathrm{~A}_m\;x^{\frac{m \pi}{a}}$
• D. $y=\displaystyle{}\sum_m\;\mathrm{~A}_{m} \;e^{-\frac{m \pi x}{a}}$