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The positive values of $\lambda$ for which the equation $y^{\prime \prime}(x)+\lambda^{2} y(x)=0$ has non-trivial solution satisfying $y(0)=y(\pi)$ and $y^{\prime}(0)=y^{\prime}(\pi)$ are

1. $\lambda=\frac{2 n+1}{2}, n=1,2, \ldots$

2. $\lambda=2 n, n=1,2, \ldots$

3. $\lambda=n, n=1,2, \ldots$

4. $\lambda=2 n-1, n=1,2, \ldots$
in Differential Equation by Expert (2.4k points)

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