First order homogenous equations 2

Another example of using substitution to solve a first order homogeneous differential equations.

Category:

Education

Tags:

• homogeneous
• differential
• equations

[fermixx]

ppl arguing about pronunciations are those who are not paying attention to the subject itself.

to be honest, my mind is focused on dif eqs so actually it doesnt matter how he pronounces/spells words. Im focused on the numbers instead !

something wrong in the numbers would be something to discuss here, because its what really matters here

[lauralew2222]

How can you tell the difference between a homogeneous DE and an exact DE when they are not in their usual forms by looking at it right away?

[subhaniawan]

sir i owe you my grades , thankyou so much

[BannedLol4l]

@psychojoshie I know it's been a year but whatever...

ln|C| actually can take on any value between -infinity and +infinity, because the range of the ln|C| function is all real numbers (graph it).

[Exploratorius12]

@Dunnylaaaaaaaaaaaaad he brings all the 'v's to the left hand side by dividing both sides by 1+v^2. thus the right hand side becomes (1+v^2)/(1+v^2) which is 1.

[Dunnylaaaaaaaaaaaaad]

I think the line at 3:43 is wrong, because he says to bring all the v's to one side, when he brings the 1+v^2 over.. why does the equation equal to 1?? should it not equal to 0?? Should he not just bring the v^2 over and leave the 1 where it is???

[AllRiffRaff]

@chemicalsymphony because if you substitute (1+v^2) with lets say "u". equation becomes (2v/u)dx. so u = 1+v^2. differentiate this you get du/dx = 2v, then du = 2vdx. then equation becomes (1/u)du. which you integrate to become ln(u). substitute 1+v^2 back in for u and you get ln(1+v^2)

[Exploratorius12]

@chemicalsymphony notice that you get the enumerator if you derive the denominator: (1+v^2)' = 0 + 2v = 2v

so basically you got something like f'(x)/f(x) with f(x)=1+v^2 and f'(x)=2v. it happens that ln(f(x)) is its 'anti-derivative' why? well if you derive ln(f(x)) by using the chain rule you get 1/f(x) * f'(x) which is the same as f'(x)/f(x). so the solution is ln(f(x)) which is ln(1+v^2)

[shapeurmind]

@chemicalsymphony I don't understand it either. I got 1/2 ln(1+v^2) .....

[add1c7i0n]

youre such a G khan. love u buddy

[chemicalsymphony]

how is the anti-derivative of 2v/(1+v^2) = ln(1+v^2)?

[JCP598]

Why is the term (2 x v v´/1+v^2) in 3:55 equal to 1 and not 0? That´s the only point I´m not getting in this video :( Other than that THANKS! You´re saving my engineers career. It´s just frustrating when teachers talk in their own math terms and you don´t get a thing of an actually understandable problem. Thx!