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

2670 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Find the general solution of the differential equation d^2y/dx^2 - 5*dy/dx + 4y = 2x


How do you show that the centre of a group is a subgroup


A child weighing 50kg is pushed down a 2m long slide (u=0.1), angled at 45 degrees from the horizontal, at 5m/s. At what speed does the child reach the bottom of the slide?


Use the geometric series e^(ix) - (1/2)e^(3ix) + (1/4)e^(5ix) - ... to find the exact value sin1 -(1/2)sin3 + (1/4)sin5 - ...


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences