Consider the boundary value problem for the deflection of a horizontal beam fixed at one end,

\[\frac{d^{4} y}{d x^{4}}=C, \quad y(0)=0, \quad y^{\prime}(0)=0, \quad y^{\prime \prime}(L)=0, \quad y^{\prime \prime \prime}(L)=0\]

Solve this problem assuming that \(C\) is a constant.