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)at+ c .                       Where c is an integrating constant.                     x(t)=Aexp(-(1/2)at2).                    Define A = exp(c).

Answered by Cal L. Maths tutor

4049 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the value of 4!/0!


Prove or disprove the following statement: ‘No cube of an integer has 2 as its units digit.’


What are the advantages of using numerical integration (Trapezium rule, Simpson's rule and so on) over direct integration?


Event A: a customer asks for help. Event B a customer makes a purchase. We know: p(B) = 0.2 and p(A) knowing that he has asked for help is 75%. What is the probability of a customer to ask for help and make a purchase?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences