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

6664 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

You are given a polynomial f, where f(x)=x^4 - 14x^3 + 74 x^2 -184x + 208, you are told that f(5+i)=0. Express f as the product of two quadratic polynomials and state all roots of f.


Why does matrix multiplication seem so unintuitive and weird?!


By Differentiating from first principles, find the gradient of the curve f(x) = x^2 at the point where x = 2


Integrate xcos(x) with respect to x


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