Give the general solution to (d2y/dx2) - 2dy/dx -3y = 2sinx

Using the auxiliary equation t^2 - 2t - 3t = 0  t therefore is equal to 3 or -1. Using this value, a complementary function is derived.  Y= Ae^(3x) + Be^(-x). Finally, to fully solve, a particular integral of y = asinx + bcosx and differentiate it twice, to give equations for Dy/dx and (d2y/dx2). These can be substituted into the initial differential equations to find the values of a and b, Which are -2/5 and 1/5 respectively. The answer is then the complementary function plus the solution to the particular integral y = Ae^(3x) + Be^(-x) + (1/5)cosx - (2/5)sinx

BY
Answered by Bradley Y. Further Mathematics tutor

8919 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Prove that (AB)^-1 = B^-1 A^-1


How do you sketch the graph of y=(x-1)/(x+1)?


Cube roots of 8?


Using a Taylor's series or otherwise; derive Euler's Formula


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