Find the general solution to f''(x)+ 3f'(x)+ 2f(x)=0

Firstly, I haven't seen the notation I used in alevel but I just used it for the sake of ease of typing it online.1st. Sub in the trial solution f(x)= Ae^(mx) and its derivatives- f'(x)= Ame^(mx) and f''(x)= Am^(2)e^(mx). Simplify by dividing by Ae^(mx) to get m^2+ 3m + 2= 0.Solve the quadratic by inspection to the solutions m=1 and m=2. Since when each solution is substituted into the original differential the result =0 we can say that the sum of the solutions is correct. (0+0=0). So the solution is f(x)= Ae^x +Be^2x

JD
Answered by John D. Further Mathematics tutor

3627 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

A 1kg ball is dropped of a 20m tall bridge onto tarmac. The ball experiences 2N of drag throughout its motion. The ground has a coefficient of restitution of 0.5. What is the maximum height the ball will reach after one bounce


Show that the set of real diagonal (n by n) matrices (with non-zero diagonal elements) represent a group under matrix multiplication


Solve this equation: x^2 + 2x + 2


Given the equation x^3-12x^2+ax-48=0 has roots p, 2p and 3p, find p and a.


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