How would I solve the following equation d^2x/dt^2 + 5dx/dt + 6x = 0

Our given equation is d2x/dt2 + 5dx/dt + 6x = 0, which we need to recognise as a second order differential equation. Therefore we need to begin by solving the auxilary funtion m2+5m +6= 0. ( Side note: Most of the mathematical equations we solve are expressed in x and y, but in this equation it's expressed in terms of x and t, where x is the dependent variable). Solving the auxiliary funtion gives us values of -3&-2 for m. Because these are real values that are not equal to each other we can use the complimentary funtion y= Aect + Bedt where y is the dependent variable, t is our independent variable and A&B are constants of intergration. If we plug in our values the auxiliary funtion becaomes x = Ae-3t+Be-2t. Which is our final answer.

DM
Answered by Dimuthu M. Further Mathematics tutor

5887 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

A curve has equation y = ax^2 + 3x, when x= -1, the gradient of the curve is -5. Work out the value of a.


Prove that sin(x)^2 - 5cos(x)^2 = 6sin(x)^2 - 5


Factorise the following quadratic x^2 - 8 + 16


Find the coordinates of any stationary points of the curve y(x)=x^3-3x^2+3x+2


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning