Auxiliary equations with repeated complex roots, Sect4.3#37a

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Auxiliary equations with repeated complex roots,
solve a 4th order linear differential equation,
higher order differential equation,

blackpenredpen

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Your channel is so refreshing. I asked my teacher if the same thing would happen for repeated complex roots as with real ones and he didn’t understand my question. The same thing does happen! 😂

darcash

Thank you so much sir for this Linear Differential Equation
This helped me a lot in my engineering examination
Thank you

rushikeshpatil

I was just recommended this video and I got this question on my exam today... before I watched this video! I haven't gotten it back yet, but I got this answer!

Loki-

If you people are not helping us it would be impossible for many students to learn something whom professors are not helping them. Thank you

sibghatullahsindhu

And why do we separate the expression for the general solutions and treat them like they are independent from each other? How do we know that will be a solution "a priori"?
Edit: So wait, like when we join "different" solutions together by adding them up when they are initially "separated" and attach coefficients to them that vary independently, are we just doing the inverse here ? Is it also correct? Why can we do this?

tanabatagaming

I am confused... can the C1 next to the cos(t) be complex? All the constants must belong to the same set right?And there cannot be constants belonging only to IR and others belonging to IC, right? I feel kinda hardcoded to believe that, because one of the the general solutions to one of these equations is e^((bi)t), (or also that same result multiplied by some function that we determine in order to make it linearly independent from the other one, like in this case, when r is the same), (and, in this case, "a" is zero so I am ignoring, because it will just be 1 multiplying the rest), cos(t) cannot possibly be multiplied by the imaginary unit because of the euler formula.

tanabatagaming

What if you have a real root and two complex roots. How do you write the solution, then?

diana.bacircea

nice video, btw you should start pde videos like basics and examples (no theory)

Lklibertad

beta=+ and - 1, sign of c4tsint should be - ?

amishaagrawal

But i and -i arent repeated roots, they are simply complex conjugates

mahfuz

Y 4th derivative + a times y = 0

Plz sir solve this🙏

parthparmar

are these constants real or complex? Can anyone help?

NirvanaGuha

Auxiliary equations with repeated complex roots, Sect4.3#37a

Auxiliary equations with repeated complex roots, Sect4.3#37a

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