Find the general solution to: d^(2)x/dt^(2) + 7 dx/dt + 12x = 2e^(-t)

"General Solution = Complimentary Function + Particular Integral"AE: m2 + 7m + 12 = 0 solve for m(m+3)=0m = -4 or -3Hence the Complimentary Function = Ae-4t + Be-3t
PI: [substitute u=ke-t]u'=-ke-tu''=ke-t[Comparing coefficients we get:]k-7k+12k=2Hence, k = 1/3.PI = 1/3 * e-tSo the general solution is:x=Ae-4t + Be-3t+ 1/3 * e-t

EO
Answered by Edward O. Further Mathematics tutor

2788 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Prove by induction that for all positive integers n , f(n) = 2^(3n+1) + 3*5^(2n+1) , is divisible by 17.


Explain why the equation tanx + cotx = 1 does not have real solutions.


Find the general solution of y'' - 3y' + 2y = 2e^x


In simple harmonic motion, where would the object have the largest speed. If the angular velocity is 2 rad s^-1, and the amplitude is 1m, what is the largest speed obtained by the object?


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