If I have a Stochastic Differential Equation such as:
$dX_t=(W_{t}^{3}+t^2)dt-2dW_t $ with $X_0$=$1$
and
$dX_t=(W_t+t)dt+W_{t}^{2}dW_t $ with $X_0$=$1$
I would not be looking for the solution.
However, how would I justify if or if not a formula for $X_t$ exists of the form $X_t = f(t,W_t)$
Thank you for your help.