I am trying to find a solution (either weak or strong) of following SDE:
$$ \mathrm{d}X_t = \tanh(X_t) \ \mathrm{d}t + \mathrm{d}W_t, $$ where $W_t$ denotes the Wiener process.
My Attempt:
I tried to use the Girsanov theorem (similar to the post in Link) to find a weak solution and I got stuck at evaluating the following integral: $$ W_t = X_t - X_0 - \int_0^t \tanh(X_s) \ \mathrm{d}s. $$
This is the Riemannian integral but it also has $X_s$ therefore, I am confused.
I am new to this area so any ideas or pointers to any books are welcome. Thank you.