I am in trouble with my homework, the quesetion is to solve a pair of stochastic differential equation.
$dX_t^1 = X_t^2dt + \alpha dB_t^1$
$dX_t^2 = -X_t^1dt + \beta dB_t^2$
$\alpha \ and \ \beta$ are constants, $B_t^1, B_t^2$ are independent standard Brownian Motion
I have tried my best to solve them, I guess I need to multiply a integrating factor, but I can not find it.