Session 19: Second order Homogeneous Linear differential equation with constant coefficients!!

In this video, we will talk about the method which will help us to find the solution to second-order linear homogeneous differential equations with constant coefficients.
First, we find Auxillary equation then on the behavior of roots of auxiliary equations we determine 2 linearly independent solutions of given differential equations. The behavior of roots will depend on the discriminant of the quadratic equation.
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link for Basis and General Solution:

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Link for reduction to first order:

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Link to reduction to first-order- Part II

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Link to Wronskian:

[profabhishekiitr]

Till now, I haven't seen a better video on concept of various cases of second order homogeneous differential equation with constant coefficient. Thank you Sir.

[simranmanghwani]

1) y(x) = c1 e^(-3x) +c2 e^(-4x)
2) y(x)= (c1+xc2) e^(-7x)
3) y(x) = e^(-3x)[Acos(2x)+Bsin(2x)]

[dakshveersinghchauhan]

You are a lifesaver, sir. Everything was very well explained.

[Yellow_tiger_]

Sir you can't imagine how much I'm thankful to you.😭😭
Thank you so much sir❤.

[rudrakshadixit]

8:33 Subtle flex with the dotted lines😅👍

[chinmaypande]

sir, while explaining 2nd condition you have taken formulae for small u which is actually of big U na?and u should be integration of U na ?, so small u comes out to be x^2/2 and not x ?.

[madhavigole]

1) y=c1e^(-3x)+c2e^(-4x). 2)y=(c1+xc2)e^(-7x).

[jaijinendra]

Thanks for the lecture, you teaches too good...👍

[lpuwallah]

such a well explained derivation and questions

[kanchanthakur]

Sir please tell method you mentioned in this video can be used for non constant coefficients?

[sohammahure]

Sir at 13:22 you wrote two format of writing the answer in which one contains i and other did not. Which one is correct sir, can you please explain?

[aishwaryavpkadam]

Sir, at 12:39 B=i(C1-C2) so it has iota in it... general solution consists of complex number na?

[aakankshasonawane]

1.y(x)=c1.e^(-4x)+c2.e^(-3x)
2.y(x)=e^(-7x)[c1+x.c2]

[soubhagyaranjansethi]

thankyou sir and keep uploading for us.

[ratneshkumar]

Sir plz provide me previous video of this so i could easily understand

[sanketgore]

Sir in context of dependent functions, if one of the function is "zero" then are the given functions always depend??