$.$ The Brownian Bridge. For fixed a$,$ b consider the following equation

dXt $=$

b Xt

$1$ t

dt $+$ dWt$.(1)$

$($a$)$ Show that

Xt $=$ a$(1$ t$)+$ bt $+(1$ t$)$ Z t

$0$

dWs

$1$ s

solves equation $(1).$