Find the general solution to the second order differential equation x'' - 2x' + x = e^(2t).

Firstly, note that the question only asks for the general solution (G.S.) to the equation, not for the whole solution. Now we have established what we need to find, construct the auxiliary equation. For this ODE, it will be k^2 - 2kx + 1 = 0. Solving this auxiliary equation, we find we have (k - 1)^2 = 0 and a repeated root solution of k = 1. Now, the form of the G.S. for repeated roots is (A + Bt)e^(kt) and substituting our value for k, we find the general solution for this ODE is x = (A + Bt)e^(t).

AB
Answered by Amy B. Further Mathematics tutor

4155 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Integrate ln(x) with respect to x.


What is the modulus of 3+4i?


What is the value of x from (x+2)^2=4


How do I know which substitution to use if I am integrating by substitution?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning