Auxiliary Equation, Repeated Roots - Differential Equations

A lecture about the solution of higher order DE using auxiliary equation with repeated roots

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For more Differential equations tutorials:

Coefficients Linear in Two Variables - Differential Equations

Homogeneous DE with Constant Coefficients - Auxiliary Equations (Distinct Roots):

Newton's Second Law in DE:

Mixture of non-reacting fluids:

Orthogonal Trajectories:

Continuous Compound Interest - Application of DE

Integrable combinations solutions to DE:

RC Cicruits in Application of First Order DE:

RL Circuits in Applications of First Order DE:

Laws of Growth and Decay:

Newton's Law of Cooling:

Bernoulli's Differential Equation:

Non-Exact DE made Exact using Integrating Factors:

Exact DE:

First Order Linear DE:

Homogeneous DE:

Variable Separable:

Family of curves:

Elimination of Arbitrary Constants:

Elimination of Arbitrary constants by Determinant Method:

Introduction to DE:

[abatandchill]

Correction, Answer in number 3 must be: y = C1e^x + (C2 + C3x + C4x^2)e^2x.
Since the root m2 = m3 = m4 = 2 and repeating. Thanks

[subamarkchristians.]

Thank you so much sir, sa effort nyo po na magturo. Napakalaking tulong po sa amin ito upang madali nming maunawaan mga lessons lalo nanpo ngayong pandemic. Ayon po, naway ibless pa po kayo ni Lord, pati ang family nyo po. maraming salamat po ulit engr. abat😇

[Starriray]

Thank you po, na 1 take ko po yung differential equation 😭❤️

[Clintlegend]

Thank u so much!!and a grt quote from the bible too!

[meliodas-sama]

Sa 11:14 po pwede rin po gamitin yun 2 as divisor sa synthetic divison. Pano po gagawin since pwede yun +1 and +2?

[liemueldeynnburgos]

Good day Sir. Yung sagot po ata sa pinasagot mo po sa amin is C3xe^3x + (C1 + C2 + C4x^2)e^-2x. Yung m1 ko po is -2 po.

[bdyhpgj]

Thank you so much, Sir! Very helpful esp during this online learning. Engr. can you make videos about Auxilary equation: Distinct and Repeated Imaginary Roots?

[jeffreysoriano]

What if a polynomial is not factorable. What should I do?

[francine]

Thank you po Sor, marami po akong natutunan. Pwede po mag ask sir? What if pinapahanap value ni C?

[timbalzodelfrancis]

Sir upload po kayo ng video about auxiliary equation: imaginary roots. Thank you po ❤️

[AexAtYourService]

Sir, bat di na available yung distinct video?

[_bieelove]

Dynamics of Rigid Bodies po engr. Thank you po

[HavilaCaeta]

Hello po sir. Mayroon din po ba kayong video for distinct and repeated quadratic factors po?

[megarbiojosephine]

Boss upload po kayo ng Non homogeneous higher order differential equations sir, yung mayredundancy . Sana po mabasa niyo. Maraming salamat po. Laking tulong po mga video niyo sakin. Godbless po.

[rabbanjuarez]

Eng. Abat Bakit wala kang Case 4 Video Sana Mag upload ka ng Case 4 .

[ronamaerecalde]

Pano po if Yung case is "The Equation has conjugate complex roots: 𝒎 = 𝒂 ± 𝒃𝒊" and ang general solution niya po is "𝑦 = 𝑒^𝑎𝑥(𝐶1𝑐𝑜𝑠𝑏𝑥 + 𝐶2𝑠𝑖𝑛𝑏𝑥)
" cosine po ba lagi dapat ang nauunang isulat instead of sine? Or pwedeng mauna yung sine instead of cosine?

[benedictmaddara]

Sir 'yung last problem po? hindi ba dapat: C1e^3x+C2e^-x +C3e^-x +(c4+c5x)e^-1/2x dapat? distinct po kasi yung m3 kaya hindi po dapat C3xe^-x?

[tian]

Upload po kau ng Repeated and Complex Roots at Complex Roots at Real and Equal roots

[rogreasonda]

Sir upload po kayo ng video about auxiliary equation: imaginary roots. tapos repeated roots an may conditions po sana thank you po.

[vinzemontydelacruz]

Strength of materials next vid engr. thankyou and godbless!