Find the solution the the differential equation d^2y/dx^2 + (3/2)dy/dx + y = 22e^(-4x)

We first find the complementary function by guessing y=e^(kx). Substituting this into the equation d^2y/dx^2 + (3/2)dy/dx + y = 0. we find k^2 + (3/2)k + 1 = 0 which factorises into (k+2)(k+1/2). So our complementary function is y= Ae^(-2x) + Be^(-x/2). Now we find any particular integral by guessing y = Le^(-4x). Substituting this in to the equation d^2y/dx^2 + (3/2)dy/dx + y = 22e^(-4x) we find that L(16e^(-4x) - 4e^(-4x) + e^(-4x)) = 22e^(-4x) and L=2. So the solution to the differential equation is y= Ae^(-2x) + Be^(-x/2) + 2e^(-4x) //

NE
Answered by Nathan E. Further Mathematics tutor

6652 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

You have three keys in your pocket which you extract in a random way to unlock a lock. Assume that exactly one key opens the door when you pick it out of your pocket. Find the expectation value of the number of times you need to pick out a key to unlock.


Given that the equation x^2 - 2x + 2 = 0 has roots A and B, find the values A + B, and A * B.


How to calculate the integral of sec(x)?


A useful practice: how to determine the number of solutions of a system of linear equations beforehand


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