I have to solve:
$dX_t=(4t-3X_t)dt+2tX_tdW_t=4tdt-X_t(3dt+2tdW_t)$
Let $$Y_t:=X_t \exp\Big(-3t-\int_0^t2sdW_s+\frac{2 t^3}{3}\Big)$$
$dY_t=X_td\Big[\exp \Big(-3t-\int_0^t2sdW_s+\frac{2 t^3}{3}\Big)\Big]+\exp\Big(-3t-\int_0^t2sdW_s+\frac{2 t^3}{3}\Big)dX_t+d\Big[\exp \Big(-3t-\int_0^t2sdW_s+\frac{2 t^3}{3}\Big)\Big]dX_t=$
Is this the only correct approach? Calculations will be very extensive. Maybe there is a simpler way?