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).
CL
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