Consider a differential equation where dx/dt = -axt. Find an equation for x(t).

Starting from dx/dt = -axt.                                We treat dx and dt as infinitessimal factors of x and t, therefore fundemental mathematical operations still apply. Rearranging the equation to group x, dx and t, dt. 1/x dx = -at dt.                               Note: We could rearrange with a on the left handside but since we want to find an equation for x(t) it is convienent to seperate all constants.                             We now have the integral:           S 1/x dx = -a S t dt.                            ln x =-(1/2)at²  + c .                       Where c is an integrating constant.                     x(t)=Aexp(-(1/2)at²).                    Define A = exp(c).