Hello, I'm new here, so I guess I should introduce myself. I'm a student at a math. finance course. We have some homework where we have to solve two stochastic differential equations, and I'm pretty stuck. Would love it if someone could show me how this is done!

The equations are the following:

$\displaystyle dX_t= \frac{b-X_t}{1-t}dt + dW_t\newline X_0 = a \in \mathbb R$

Where b is a real constant.

$\displaystyle dY_t=\frac{1}{Y_t}dt + \alpha Y_tdW_t \newline Y_0=y \in \mathbb R^+^+$

Where alpha is a real constant.

Looking forward to hearing from you!