Solution to a 2nd order, linear homogeneous ODE with repeated roots

I discuss and solve a 2nd order ordinary differential equation that is linear, homogeneous and has constant coefficients.
In particular, I solve
$$y'' - 4y' + 4y = 0.$$
The solution method involves reducing the analysis to the roots of of a quadratic (the characteristic equation). Such an example is seen in 1st and 2nd year university mathematics.

Category:

Education

Tags:

• ordinary
• differential
• equation
• ODE
• homogeneous
• second
• order
• characteristic
• calculus
• MATH2019
• mathematics
• Chris
• Tisdell
• UNSW

[1001Iruka]

Hey Dr T, that's a real nice solution.

I liked it.

Lighting on the video could be a bit better, though.

[DrChrisTisdell]

You're right, Iruka. The sound and lighting could be improved. Some of the more recently uploaded vids have better sound and lighting as I've been experimenting with simple post-production.

Thanks for posting!

[geethakaf]

MATH2019

Awesome stuff !!

Keep up the good work

[DrChrisTisdell]

Thanks!! : -)

[3d9e]

you looks nervous in some videos nevertheless very helpful videos for those hard 2019 tute problems.

perhaps your in class lecture videos could be helpful too.

[DrChrisTisdell]

Yes, I tend to feel more comfortable with a "live" audience! Later this session i will be experimenting with video recording of full lectures. Watch this space!

[JeMiodhih]

very very nice video!! thanks a lot,great help! would have been better if you had also showed the particular solution for the example also!

[zabuzamomochi55]

Dr. Tisdell, you are AWESOME!!

[dojOdRiFTeR]

@DrChrisTisdell what happens if the roots are not real for instance this one, y'' +8y' +20y =0 .

[FallofDarkness55]

thanks for these videos.

[jsm666]

You could just as easily write the general form for repeated roots as y(x) = (e^lambda.x) [A+Bx}, couldn't you? This would differentiate it from the distinct-roots solution and ensure that the x term attached to the B coefficient isn't forgotten.

[blackphoenix04]

i was in ur maths 1B back in 2007 - so when i had to relearn ODE i thought i;d google to see if u have ur lecture notes. im SO glad u have these vids up!! major help! thanks =)

[Alibey1976]

Chris,

You are doing an excellent job with your videos. I've been re-learning Math thru your ODE , Laplace and other videos. Compared to other videos in youtube, it is nice to see the person that teaches rather than only his/her voice.

Thank you from Lafayette, Indiana

Ali.

[1001Iruka]

Yes, I have noticed that the recent ones look really nice and clear.