1 1 vote For the differential equation $\dfrac{d^2 y}{d x^2}+k^2 y=0$, the boundary conditions are $y=0$ for $x=0$, and $y=0$ for $x=a$ The form of non-zero solutions of $y$ (where $m$ varies over all integers) are $y=\displaystyle{}\sum_m\;\mathrm{~A}_m\;\sin ^{\frac{m \pi x}{a}}$ $y=\displaystyle{}\sum_m\;\mathrm{~A}_m\;\cos ^{\frac{m \pi x}{a}}$ $y=\displaystyle{}\sum_m\;\mathrm{~A}_m\;x^{\frac{m \pi}{a}}$ $y=\displaystyle{}\sum_m\;\mathrm{~A}_{m} \;e^{-\frac{m \pi x}{a}}$ Differential Equations gate2006-ec differential-equations boundary-value-problems calculus + – admin 464 views answer comment Share Follow Add Sync Questions Print 0 reply Please log in or register to add a comment.
