How to use Laplace Transform to solve Differential Equations ** Full Example **

We do a full example solving an Initial Value Problem or IVP using the method of Laplace Transforms. This involves applythe Laplace Transform to the differential equation, substituting in the inital conditions, using partial fraction decomposition with an irreducible quadratic to clean up the algebra, and then doing an inverse Laplace Transform to get back to a solution of the IVP.

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This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.

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[nsworld]

Very informative video. Learnt a lot ... Thank you. But at @6:28, there is just a typo - y(s). It will be "y(t)". Right sir ? Thank you for your time.

[tuongnguyen]

I really like your lecturing style, it shown me that every act of algebraic manipulation has a PURPOSE or a specific GOAL behind it. Back in my school, we just learn by heart without knowing the idea behind stuff which is a misleading way of learning mathematic.

[islambarakat]

Really good work, it helps a lot through my study, presented by a clever mathematician. Thank you

[aashsyed]

*i'm not a mathematician * but im learning and glad i founda this channel :)

[eetulaakso]

Thank you for your video! It was very informative and I like your style how you tell and teach these. It is very enthusiastic.
I have one question about the video. You did that partial fractioning thing where you wrote A/(something) + B/(something) + Cs+D /(something). Why did you write that last term as a Cs +D, why it wasn't just C?

Thank you about this video and this whole series of Laplace transformation videos!

[aashsyed]

3:55 another fun fact about the s^2+1 it is factorable in the complex numbers! it's (s-i)(s+i) so cool!

[yasirskyrose]

ngl your video help me understand laplace transform also inverse laplace for diffr equation i have finals in a few hours idk y for the whole semester i dont understand when its this easy

[fahrenheit]

Overkill, no? This is easily doable with a characteristic equation approach. I mean, I always appreciate a good exercise but it'd be nicer to see examples where other approaches fail but Laplace gives a way in.

[NhlanhlaNdlovu-ev]

Does the Laplace Transform work for the solution of non-CCL ODEs?

[loicnasser]

Hello, and if the initial conditions are not in 0 but for example y(2) or y(7), how do we solve with this method ?

[chyldstudios]

Where did you get the math t-shirt? It rocks!

[الأستاذأحمدالرماحي-عع]

Thanks
please Can you show me the method of solving the Fredholm integral equation by Mendeleev’s Quadratures؟

[nostoon]

I'm so scared that soon I'm going to have to solve a question like that along with 10 other questions on a test that I only get 1 hour to complete.

[ayaadel]

why the last term in min 6: 30 isn't ( 1/2 e^-t * t )?