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

A video about finding the solution of a homogeneous DE with constant coefficients using auxiliary equations.

All of the examples have DISTINCT roots.

If you find this video helpful, don't forget to leave a thumbs up, comment, and kindly subscribe to my channel.

For more Differential equations tutorials:

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:

Thank you so much and God bless!

[ajjixyreneroque]

To be honest, dito ako natuto nang lubos sa DE at hindi sa class kasi nga kailangan naming madaliin lahat ng lessons, that's why kailangan mag self study. Buti nalang may ganitong videos si Engr. Thank you!

[wrightkuku]

you have no idea how this helped me ....many blessings

[victoriaivybarela]

Had to learn the auxiliary equations before jumping to second ordered differential equation haha. Big thanks sir!

[novajaneluzano]

Thank you. Big help for our final requirement. We were given ebook only for reference and its so hard to understand it. Glad i saw this.

[maryjoymakalintal]

Thank you sa lahat ng tutorials mo Sir. ♥ Ang dali nya pong maintindihan. Ang laking help nya since naka online classes. God bless always po.

[Dee-nmkt]

Anlaking tulong po ng mga tutorials mo engr. God bless you po. ♡

[alexanderjaschapamor]

Hi Sir, in number 5, you can divide the equation 4m²-14m+12 by 2 leaving 2m²- 7m+6=0
Since the last term is positive and the second term is negative, both of the factors have minus sign.
The simplified equation has a factor of (2m-3)(m-2)
The same result when you used quadratic equation.

Anyway, great job for teaching us this. I wanna be your student so bad but mighty maroons offers a free tuition, tamaraws cant relate.

[angelicacherryubenatanierl]

Thank you so much for this po. Mas naging malinaw po ngayon sa akin itong lesson na ito <3

[awiterpgamer]

Thanks po. Ngayon ko lang natutunan yung all possible roots. di na ako mahihirapang manghula ng values

[jovanmagtoto]

salamat po dito sir. Big help lalo na ngayung online class.

[jimranbautista]

Thank you Very Much Sir. Buti nalang at meron ka po na nagtuturo Ng Calculus😊

[geromegacrama]

Thank You sir, malaking tulong neto sa akin, God Bless You po🙏🙏🙏

[mariadappy]

BIG HELP PO SIR! TBH DI KO MAINTINDIHAN YUNG PROF NAMIN SA TOPIC NATO PERO SA INYO, WOAH! ANG GALING! ACTUALLY, LAHAT NG TUTORIAL VID NIYO NAPANOOD KO NA AND DITO AKO NATUTUTO HAHAHA KEEP IT UP PO! WE NEED YOU! GOD BLESS YOU PO! MORE VIDS!

[vernicea]

How about po if yung root is fraction like m= -3/2? just write it as is po ba? Also, the root is repeated but not imaginary, m=1±√6 lng

[eugineguan]

Hoping for more videos about higher order differential equations sir. Thank you!

[rhonamaehamlag]

Thnak you Sir! do you have lecture vid about Non homogeneous DE with Constant Coefficients?

[meliodas-sama]

Sa 18:22 po, pwede rin po gamitin yun -3 as divisor for the synthetic division. So pano po gagawin if pwede yun -2 and -3?

[israeleslabon]

Good evening, Sir? Can you please make a tutorial video of the Method of Undetermined Coefficient? Thank you. GOD bless you!

[Chinchan-njiz]

Hi sir! sa problem 5, I used in synthetic div the factors 2 and -1 then after that I used the quadratic in the new equation (4, -4, -3, 0) tapos yung roots ko po ay iba sa inyo wala akong 1/2 at 3/2 kasi nagiging 0 lang din naman siya sa -1 at 2 na factors. Check pa din po ba ito? my roots are (2, -1, 3, & 1)

[georgejunseneca]

thank you sir the video is a very big help, have some request sir can you do tutorials on the other cases, more power😁