Differential Equations - 24 - 2nd Order - Complex Roots (r=a+bi)

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How to solve a constant coefficient homogeneous linear 2nd order differential equation with complex roots.

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You are awesome. I've never seen someone this clearly explaining Differential equations.

srideepthiborra

Great stuff here. Has really help wrap up ideas in Diffeq. Test in 5 hours

carterfortuin

Good work mathematician comments from Tanzania i like this wonderful solution

ireneludovick

The way of explanation is so helpfulll

NK-iyif

Thank you so much for making these videos, I find them very helpful as I'm currently studying simple harmonic motion with damping. If you can make a video correlating solving 2nd order homogenous constant coefficient linear differential equations with the general differential equation of simple harmonic motion with damping, that would be really cool of you. Again, thank you so much, these videos are much appreciated!

elfishpirate

Thank you for making these videos. I'm glad you could cover everything there is to know about differential equations.

Generalth

THANK you. I was going nuts with other videos just showing the final formula without showing where it came from.

rocketpsyence

if we're given initial condition for y and y'
how do we do the y' as far as the signs go?

should it be like
y = e^(at) (c1 * cos(bt) + c2 * sin(bt) )
y' = te^(at) * (c1 * cos(bt) + c2 * sin(bt) ) + e^(at) * (c1 * sin (bt) + c2 * cos(bt) )

jacksonmadison

Taking Circuits 1 EEE202, as a Junior Mech. Eng., super helpful thank you!

CaptainMoroni

If we have 2y''-12y'+20y=40 then please tell me the solution because according to this answer is
Y=e^3t(c cost+c sint)

muntahafaisal

@The Lazy Engineer ... your videos are awesome :D ..you are really a wonderful person..thank you so much..
may i ask..what software are you using for making your videos ?
the one for writing and the one for screen casting

mazenosama

at 3:37 how do you put in that form for Euler's formula?

mollypete

Why do you need to write the solution in terms of Y a and Y b and then superimpose them to general solution y?

preethiravi

Well I pretty much didn't understand any of that.

TheBillzilla

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