Homogeneous Differential Equations (introduction & example)

A homogeneous differential equation is a differential equation in the form of dy/dx=G(y/x). We can convert this into a separable differential equation with the substitution u=y/x. This is an example of how we can solve differential equations by substitution.
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[@moldscraper]

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[@asasasas3758]

I love how when each semester ends, bprp always has just the right video for any mathematics course i have the next semester. Thank you for being who you are.

[@stevenkelty8025]

You and your david bowie ball saved me from frustration! THANKZ

[@Apple-sq4wr]

So useful! I coundn't have done it without you!

[@surojitchakma996]

Your teaching method is really helpful to me. Sir,please make a video with cosx, sinx,cosy,Sony Question like {1+xycos(xy)}dx+x Cos(xy)dy

[@schrodingerscat6119]

put y= vx and try !!!

[@alooooshm]

Very clear. Thanks!

[@sollertia_]

I've come to realize that western teachings like to substitute using u=y/x while chinese textbooks prefer y=ux.... (it doens't affect the process or answer)

[@angelmendez-rivera351]

Yes, the West likes division a lot.

[@anushaanu8697]

Thankkk uuuu soooo much.... I searched loot of videos bt... Dz video made me satisfy....

[@theson22788]

does it always work with just y/x after all the simplification

[@kennethalcause5724]

son dang nope. You can also use this for x/y by making x=uy, dx=udy+ydu, and u=x/y

[@holyshit922]

In polish textbooks there is also so called generalized homogeneous equation dy/dx=y/xf(y/x^r) , where r in R Equation in the form dy/dx=f((a_1x+b_1y+c_1)/(a_2x+b_2y+c_2)) can be reduced to homogeneous

[@1.8millionvolts87]

bro idk how he got tan in the last one

[@28rizzons]

@@1.8millionvolts87 search for the derivative of the inversa tangent, or arctan.

[@b0ld651]

trig identities @@1.8millionvolts87

[@hirahira8018]

How is appeared Tangent

[@redshell3998]

Thank you!

[@JohnKleshuviz]

thank you babes great help

[@gokul4756]

Small explanation clears my big doubt ❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️

[@jvg6877]

when he hits the marker on the board 🥰

[@kaveeshagunasinghe861]

Thank you..

[@umeshchandra1204]

thank you sir

[@schrodingerscat6119]

then it will be a fun to solve them !!!

[@kummudsharma6963]

Its vry good Sir's smile also affects in grabing solutions

[@navin1900]

what is homogenous function can u explain .Is this method have any condition to apply

[@angelmendez-rivera351]

Did you not watch the video?

[@sharmaignejimena1033]

Hi Sir.. please help me solve this. (x^2 -xy + y^2) dx - xy dy

[@vincentkanamwai1658]

excuse me madam, your equation is incomplete!!!! is it equal to .... i mean (X^2-xy + y^2) dx - xy dy = ????

[@vincentkanamwai1658]

(x^2-xy+y^2)dx-xydy=0 (x^2-xy+y^2)dx=xydy here divide both sides by x^2dx to get 1-y/x+(y^2/x^2)=(y/x)dy/dx now let v=(y/x) and y will be y= vx. to get 1-v+v^2=vdy/dx devide both sides by v (1-v+v^2)/v=dy/dx remember in y=vx, dy/dx= v +xdv/dx since here dy/dx resembles our dy/dx in earlier equation, we equivalent: v+xdv/dx=(1-v+v^2)/v subtract both sides v ((2v^2-v+1)/v=xdv/dx make each side be of the same type i.e v/(2v^2-v+1)dv=(1/x)dx now intergrate both sides [7ln16v^2-8v+8+2arctan{(4vroot7-root7)sq.root7}/7]/28=ln|x|+c then substitute v with (y/x) Am Vincent at University of Nairobi in Kenya. Any problem contact me at [e-mail]

[@林曦-s4l]

very good👨‍🎓👨‍🎓👨‍🎓

[@schrodingerscat6119]

its very easy sum man !! do that sums which are mindboggling sums !!

[@zaidabdullrahim6912]

does it always work that i can have the equation written in the form dy/dx = G(y/x)

[@danangelocajuilan1524]

Yeah the constant is G

[@angelmendez-rivera351]

No, it is not possibly to write every first order ordinary differential equation as an equation of the form dy/dx = G(y/x). This is why these have a special name: homogeneous equations.

[@rabindrasharma]

Awesome

[@ritiksingh6144]

I am from India

[@Annosj123]

5:54 please tell me what happend there?

[@Thoalfeqargamer]

اختصر ال v مع v cancellation work :D

[@nandammunni4860]

supeb teaching mam

[@ejboyedza5261]

5:53 THIS WHERE MY MIND BLOW

[@mikewheeler5014]

it is like he used dx and dv as variables and moved them to sides at which the respective variable of their derivatives are so we get that and as for integration we need we need a differential variable in the numerator we flip both sides and get the resultant equation for integration

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[@blackpenredpen]

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[@blackpenredpen]

= )

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[@schrodingerscat6119]

this sums we do in elementary level

[@Mr_Marinaru]

hmmmm, which country?

[@threesea2358]

Please speak slowly. Thank you😊

[@the.real.transformation]

thik se bola kro bhai

[@alexbeaulieu2287]

thank you my good sir