I'm in a bit of trouble with my homework and was wondering if anyone could help me find the solutions to these two stochastic differential equations. Would really appreciate it! Thanks in advance! :)
1.
\begin{cases} dX_t= \frac{b-X_t}{1-t}dt + dW_t\newline X_0 = a \in \mathbb R \end{cases} Where $b$ is a real constant.
2.
\begin{cases} dY_t=\frac{1}{Y_t}dt + \alpha Y_tdW_t \newline Y_0=y \in \mathbb R^++ \end{cases} Where $a$ is a real constant.
3.
Verify which of the processes are affine