If I have a stochastic differential equation gives as $$ dX_t = aW_t^2dt +bW_t^3dW_t$$ where $w_t$ is a wiener process and $a,b$ are real numbers. How can I reach the integral representation of $X_t$? In other words how do I compute $f,g$ such that:
$$X_t=X_s+\int_s^tf(t,W_t)dt+\int_s^tg(t,W_t)dW_t $$ when $t>s$