How to solve second order differential equations

A lecture on how to solve second order (inhomogeneous) differential equations. Plenty of examples are discussed and solved. The ideas are seen in university mathematics and have many applications to physics and engineering.

[DrChrisTisdell]

@wjc3516 Every now and then the frame rate varies (but the audio rate stays fixed), however usually things sync when I turn each page. Good luck with your studies.

[DrChrisTisdell]

You are welcome and I also encourage you to check out my new and free ebook with lots more examples.

[DrChrisTisdell]

@dachoeks3 Every now and then the frame rate varies (but the audio rate stays fixed), however usually things sync when I turn each page. Good luck with your studies.

[DrChrisTisdell]

My pleasure and hope you enjoy my new ebook also. The free download link is in the description.

[jake]

Not only did my diff eq prof schedule our midterm for 830 am the day after spring break, but he decided to throw some nonhomogeneous problems on the test, which we haven't learned yet. You just saved my life. Cheers from the Bronx.

[DrChrisTisdell]

Equate all coefficients of x[sin x + cos x] on one side of the equation with all coefficients of x[sin x + cos x] on the other side of the equation. You should be able to form the equation -4D - 2C +2D = 0 which will simplify.

[Marcinkonys]

So when equating coefficients, can you ignore any x's you have? I was trying to solve one problem involving a trig function, and in the end got sin x(-2C-4Dx+2D-2Cx)+cos x(...+2Dx)=5sin x. Basically a bunch of Cs, Ds and even x's. Could I just ignore the terms that have an x in this case?

[umersvlogs]

if we are having two trignometric functions having different angles on the right hand side of the question, then will we find Yp for both the functions and add them? correct me if i'm wrong! please

[adelsaade]

At 33:47 why you said that the roots are complex? y''+y=0 -> λ^2+λ=0 -> λ(λ+1)=0 -> the roots will be λ=0 or λ=-1

[robertogonzalez]

AWESOME VIDEO, I had an exam for getting into a Msc and I didn't remember how solving this equations, my life as student in college would be much better having professors like you, great teacher, thanks a lot you saved my life, I already download your ebook.

[sanjibmukherjee]

Sir whether it is the method of undetermined coefficients to solve for a particular solution and thanks for nice explanation.its very helpful.

[longliu]

did you find A and B before you find particular solution or after?

[asfandkhan]

what i am unable to understand is how he decides to choose which value to take as for the y(PI) like initially how to chose Cxe^(2x) OR cX^2E^(2x) for any question. Can someone please help! :(

[palmoasis]

this is the most helpful and comprehensive video i have ever watched in math on youtube literally, and i have watched alot! thanks a million, Dr Tisdell!

[DrChrisTisdell]

My pleasure and thanks for the feedback.

[jumplake]

I have an eng. maths exam in a week's time, this was so helpful - thank you!

[DrChrisTisdell]

My pleasure and hope you enjoy the new ebook also!

[melbourneopera]

thanks Mr Tisdell.. it is good to have a revise after math lecture 

[mahmutk]

I watched the video and still curious about what if y_h roots unequal and unreal. What happens the equation y_h then?

[TheMusicalAlien]

Thank you Dr.Tisdell for your great explanations~ The wide variety of examples helped to solidify my knowledge of differential equations without much prior knowledge.