Find the eigenvalues and eigenfunctions for the following boundary value problem (with $\lambda > 0$).

$$\displaystyle y''+{\lambda}y = 0 \qquad \mathrm{with} \quad y'(0) = 0, \quad y(2) = 0.$$

Eigenvalues: $\quad \,\,\lambda_n =$

Eigenfunctions: $\ \ y_n =$

    Notation: Your answers should involve $n$ and $x$.

---

If you don't get this in 2 tries, you can get a hint.

Hint: