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.

WP
Answered by William P. Maths tutor

2405 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The line l1 has equation 4y - 3x = 10. Line l2 passes through points (5, -1) and (-1, 8). Determine whether the lines l1 and l2 are parallel, perpendicular or neither.


How many solutions are there of the equation a+b+c=12, where a,b,c are non-negative integers?


Differentiate 4(x^3) + 3x + 2 with respect to x


How Do I Integrate cos(x) and sin(x) with higher powers?


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