(Sorry about my english I'm a South American student)
The deflection of a fixed beam is zero at $x=0$ and $x=L$ on its boundaries. The beam resists a distributed load of $Wo$ per unit length. The equation is:
$$\frac{d^{4}y}{dx^4}=\frac{W_{0}}{EI}$$
$$0 < x < L$$ Where $Wo$, $E$, and $I$ are constants
$y(0) = y''(0) = y(L) = y''(L) = 0$
Solve using Laplace Transform