I started learning Differential Equations just a week ago. And "2u" joke is just fine for me! This funny way is what makes learning more engaging and entertaining
@kingbeauregard
2 жыл бұрын
Really nice! I was thinking to myself, "how's SyberMath going to solve a differential equation that isn't homogeneous?" and OF COURSE the answer is, "find a way to make it homogeneous". Just a reminder, an equation is homogeneous if you can replace every "x" with "cx" and every "y" with "cy" and all the c's cancel each other out.
@Blaqjaqshellaq
2 жыл бұрын
Furthermore, you can put the logarithms on the same side to get arctan[(y-1)/(x+4)]=ln[(x+4)^2 + (y-1)^2]^1/2 + C.
@jarikosonen4079
2 жыл бұрын
But no isolation of 'y'?
@Vladimir_Pavlov
2 жыл бұрын
The delight of the neophytes is so touching. They saw the application of one of the standard methods from the first-order ODE theory. And if so, dy/dx= - (e^x+y+3)/(x-y+5) .
@laurentthais6252
Жыл бұрын
The general method to solve this is the change of variables x=u+h, y=v+k imposing h+k+3=0, h-k+5=0, hence h=-4, k=1. You then get an homothetic equation dv/du = f(v/u) which is solved by the next change of variable t=v/u. This works only when the determinant of the linear forms is non-zero. In the degenerate case where it is zero, e.g. the 2 linear forms are proportional, the change of variable u= one of the linear forms without the constant brings you to a separable first order ode.
@Rbmukthegreat
2 жыл бұрын
Very nice! My intro to differential equations starts next Wednesday, so this video is very timely!
@kingbeauregard
2 жыл бұрын
What SyberMath isn't teaching is the thousand and one techniques to solve differential equations. What he's teaching is how to wrestle an equation into submission so that it can then be subject to differential equation techniques. So that's the thing to get from these videos IMHO: be creative in your approach.
@Rbmukthegreat
2 жыл бұрын
@@kingbeauregard after a year of watching this channel, I 100% agree with this! All of sybermaths videos demonstrate amazing creativity, and I can say I’ve learned a lot.
@SyberMath
2 жыл бұрын
Thank you! 🥰
@elphusmasete7692
Жыл бұрын
I just like the way he solve Diophantine equations
@dublistoeo
2 жыл бұрын
Hey, I like the jokes about 2u or 2b or not 2b.
@tulbanhawk
2 ай бұрын
FYI, probably should be inferred that x, y are *real* Long story short, if complex solutions are acceptable, I found a complex (perhaps singular?) solution: *y = 1 ± i (x+4)* (didn't check for homogenous solution and +C) The substitution I used is most likely incorrect: z = x - y + 5 and go from there, and after proper subs, one could assume that the solution is a polynomial, can be shown deg [z] = 1 z = ax + b OR assume that y = ax+b, which is even faster to solve, and Bob's your uncle :D
@KJIUYHN
2 жыл бұрын
this solving was very educational.
@esteger1
2 жыл бұрын
Thanks a million! This is the best video I've seen so far.
@SyberMath
4 ай бұрын
Thank you! ❤
@yoav613
2 жыл бұрын
You can not isolate y,but you can find a private solution: y= ix +(1+4i). Then y'=i, and ((1+i)x+(4+4i))/((1-i)x+(4-4i))=i
@peterbyrne6394
Жыл бұрын
Hi Your exercises are pretty difficult always. However thanks.I appreciate your cleverness.
@SyberMath
Жыл бұрын
You are welcome!
@highmind2792
2 жыл бұрын
I hate the condition tan-1 , prefer arctan specially when there is powers in the equation
@kodirovsshik
2 жыл бұрын
Arc gang here
@highmind2792
2 жыл бұрын
@@kodirovsshik Where is he?☺
@michaelbaum6796
5 ай бұрын
Great presentation, thanks a lot👍
@SyberMath
5 ай бұрын
Glad you liked it!
@scottleung9587
2 жыл бұрын
I got y=+-sqrt(6x-x^2+25)+5...didn't need any of that substitution or trig crap.
@kodirovsshik
2 жыл бұрын
You have probably made a mistake somewhere as this doesn't seem to solve the equation stated. Have you plugged it back to check the correctness?
@scottleung9587
2 жыл бұрын
@@kodirovsshik I don’t know if I could plug it back since it’s quite complicated, but I cross-multiplied and integrated both sides. From there, I separated the y terms from the x terms which is how I got my answer.
@jamesstrickland833
2 жыл бұрын
@@scottleung9587 cross products won't work since the dx and dy would distribute in a way that makes them inseparable.
@kodirovsshik
2 жыл бұрын
@@scottleung9587 > but I cross-multiplied and integrated both sides How would you do that? One would need to take integrals of x dy and y dx, which is not xy+C, because x and y are not independend
@user-nl7mn4rr6s
2 жыл бұрын
you can combine 2 ln form
@vaibhavkrupakar240
2 жыл бұрын
Or you can take x-y+5=t and differentiate with respect to x and substitute and we will.get the values
@ngichengchingnen1436
Жыл бұрын
01:24
@NecmettinMarmara-Fizikci
2 жыл бұрын
Thanks subermath
@SyberMath
4 ай бұрын
No problem Necmettin hoca 😄
@abdoshaat3304
2 жыл бұрын
You change the postulate of the problem and direct it upon your wishes
@SuperYoonHo
2 жыл бұрын
Hey SyberMath, awesome video!
@SyberMath
4 ай бұрын
Thank you! ❤
@highmind2792
2 жыл бұрын
Hello everyone. Someone can help I define perfect difference factor number (PDFn) like 392 which has the follow properety: 392 factors is: (n, 392/n) namely: 2×196 =4×98 =7×56 =8×49= 14×28 the differences of factors (n,392/n) is 194, 94, 48 , 41 , 14 the sum of difference factors(plus first factor 1) is 1+194+94+48+41+14=392 Then 392 is PDFn. its the first number with this properety , the next is over 10^10. Is there next one number??
@owen7185
2 жыл бұрын
You're definitely next level, excellent teaching and explanations
@SyberMath
2 жыл бұрын
Wow, thank you!!! 🥰🧡
@murad4622
Жыл бұрын
Really nice
@SyberMath
Жыл бұрын
Thanks a lot
@subhashkumarsinha8252
Жыл бұрын
Excellent
@SyberMath
4 ай бұрын
Thank you! ❤
@rabindranathbrahmachari9503
2 жыл бұрын
Thank you sir
@SyberMath
4 ай бұрын
Of course!
@mcwulf25
2 жыл бұрын
Nice explanation. But what a messy answer!
@yoav613
2 жыл бұрын
Perfect!
@SyberMath
4 ай бұрын
Thank you! ❤
@charlesgodswill6161
2 жыл бұрын
Would the substitution of y=vx work in converting it to homogenous ODE?
@yassinezanned9837
2 жыл бұрын
No, that wouldn't work because the 3 and 5 on the top and the bottom will ruin the substitution for you. Basically an x will be factored out of y (which you want to substitute) and x itself (on the top and the bottom) but not out of both of the numbers 3 and 5. If you couldn't understand what I'm saying you can write it on a paper and hopefully you'll get my point. Cheers!
@charlesgodswill6161
2 жыл бұрын
@@yassinezanned9837 been struggling to apply y=vx and I’ve been stuck since yesterday. 3 and 5 are making things ever harder. It doesn’t even lend itself to partial fraction for easy manipulation
@yassinezanned9837
2 жыл бұрын
@@charlesgodswill6161 Exactly, that wouldn't help you to do partial fraction, thus the substitution wouldn't work in this case. Have a great day 😊
@barakathaider6333
2 жыл бұрын
👍
@tbg-brawlstars
2 жыл бұрын
I literally understood nothing in this video cuz I don't know Integration yet. Just a year more to come to Integration chapter....
Пікірлер: 58