For the differential equation $\frac{d^2y}{dx^2}$+ k²y = 0 the boundary conditions are (i) y = 0 for x = 0 and (ii) y = 0 for x = a The form of non-zero solutions of y (where m varies over all integers) are

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y = $\sum_m A_m sin \frac{m \pi x}{a}$

For the differential equation $\frac{d^2y}{dx^2}$+ k2y = 0 the boundary conditions are (i) y = 0 for x = 0 and (ii) y = 0 for x = a The form of non-zero solutions of y (where m varies over all integers) are