Given a second order Differential Equation, how does one derive the Characteristic equation where one can evaluate and find the constants

Given a ODE of the 2nd order, Ay''+by'+cy = 0, we assume the general solution of the exponential form y=e^(mx).As we will see this leads to an easy simplification due to the properties of the exponential . From this we substitute in and we get Am^(2)(e^mx) +bm(e^mx) + c(e^mx) = 0 here we have a like term of e^mx and thus can be eliminated leaving a quadratic of the form Am^2 + Bm + C = 0 where for a particular ODE we can solve quadratically and will have two values of m for a well-defined solution of the ODE.

Answered by William P. Maths tutor

2238 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do you integrate by parts?


Integration question 1 - C1 2016 edexcel


Find the constant term in the expression (x^2-1/x)^9


Use implicit differentiation to find dy/dx of the equation 3y^2 + 2^x + 9xy = sin(y).


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