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

Related Further Mathematics A Level answers

All answers ▸

Solve the second order ODE, giving a general solution: x'' + 2x' - 3x = 2e^-t


Find the derivative of the arctangent of x function


A=[5k,3k-1;-3,k+1] where k is a real constant. Given that A is singular, find all the possible values of k.


Using the substitution u = ln(x), find the general solution of the differential equation y = x^2*(d^2(y)/dx^2) + x(dy/dx) + y = 0


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