The question is to solve the 1-D SDE $$ dX_t = \mu_t X_t dt + \alpha_tX_tdB_t^1 + \beta_t X_t dB_t^2, \quad X_0 = x_0, $$ where $\mu, alpha$ and $\beta$ are (nice) deterministic functions and $B=(B^1,B^2)$ is a 2-D standard Brownian motion.
Down below is my way of expressing this Geometric Brownian motion (and the teacher's solution):
Isn't this the exact same way of expressing one and the same thing? Or am I missing something obvious that makes my way of expressing it incorrect by not using the integrals?
Best regards