Yeah, that’s fine. I mean technically you’re dividing by 0, but, for one you can always say: suppose our solution is only defined on (-pi/2,pi/2). Also the goal of this problem is to find a formula for the solution. Once you found that formula you can then legitimately check if it solves the differential equation or not.
Dr, porque no mejor sustituyo el valor de y1 en la ecuación en vez de aplicar la regla de derivación de dos funciones, en la parte donde ya tenia una expresión para el wrounskiano y se simplificaba mucho la solución.
Neat! Now I can research under what circumstances (if possible at all) both solutions could be the same, and if that is an indication of something special going on. :)
I have to strongly disagree. Even in prime notation the dx in integrals is an integral part of the notation. He even uses it ( 9:47 on the top blackboard) but still forgot it at some point.
I couldn't figure out what Peyam was eating. It sounded like "iced meat fresh signature" which sure didn't sound like food to me. I typed it into a search bar and sure enough found meetfresh signature herbal jelly (cold)! Huh. meetfresh.net/Menu/Herbal-Jelly/Signature-Herbal-Jelly
y''-tan(x)y+2y=0 The other technique for solving it is change of independent variable t=tan(x) dt/dx=1+tan^2(x) dt/dx = 1+t^2 dy/dx = dy/dt*dt/dx dy/dx = (1+t^2)dy/dt d^2/dx^2 = d/dx(dy/dx) d^2/dx^2 = d/dt((1+t^2)dy/dt)(1+t^2) d^2/dx^2 = (2t dy/dt + (1+t^2)d^2y/dt^2)(1+t^2) (1+t^2)^2d^2y/dt^2+2t(1+t^2)dy/dt - t(1+t^2)dy/dt+2y=0 (1+t^2)^2d^2y/dt^2 + t(1+t^2)dy/dt + 2y = 0 Now it is easier to solve by series expansion
Finding the second solution through Wronskian is really amazing. Good show.
Whitechalkblackboard
Wonderful, and I love your enthusiasm and excellent teaching skill!
love your videos!!! keep it up peyam 💪
jumping to Step3: you divide by y1² to get to use the quotient-rule.. but y1=0 at -PI/2
Yeah, that’s fine. I mean technically you’re dividing by 0, but, for one you can always say: suppose our solution is only defined on (-pi/2,pi/2). Also the goal of this problem is to find a formula for the solution. Once you found that formula you can then legitimately check if it solves the differential equation or not.
okay, thanks :) Dankeschön, Grüße aus Thüringen in Deutschland :)
In which cases can you use the Wronskian? is it a general method for finding other solutions by knowing one of them?
Daniel Borrero This works for any n-th order linear homogeneous ODE where you already know n-1 solutions and you need to find just one more :)
Dr. Peyam's Show thanks I love your videos 😀
can u do a video on this integral....
integrate(x^2+6)/((xcosx-3sinx)^2)
i asked blackpenredpen earlier!!!
I'll do a video on it (if I figure it out)
who is this??😊😊
A math youtube channel.
okkk
Its crazy and awful when there are any coefficients (with derivatives) being the functions, but not numbers) Thank you for video)))
Dr, porque no mejor sustituyo el valor de y1 en la ecuación en vez de aplicar la regla de derivación de dos funciones, en la parte donde ya tenia una expresión para el wrounskiano y se simplificaba mucho la solución.
So is it correct to assume that there can be only 2 solutions, because the differential equation is of second order? (If that's the correct term.)
Basically yes, this follows from what's called the existence/uniqueness theorem for ODEs! :)
Neat! Now I can research under what circumstances (if possible at all) both solutions could be the same, and if that is an indication of something special going on. :)
9:06 what?
you forgot dx in your integrals! Angry reacc only!
Leonard Romano That's because it is in the prime notation and not dx notation.
I have to strongly disagree. Even in prime notation the dx in integrals is an integral part of the notation. He even uses it ( 9:47 on the top blackboard) but still forgot it at some point.
My professor in Integral Calculus doesn't use dx in prime notation.
I would love to be a student in his classes man.
First like and comment. I love the video. And adore the scene with Want to find.
that intro laugh lol
Big virtuosity. Thanks.
Good
I couldn't figure out what Peyam was eating. It sounded like "iced meat fresh signature" which sure didn't sound like food to me. I typed it into a search bar and sure enough found meetfresh signature herbal jelly (cold)! Huh. meetfresh.net/Menu/Herbal-Jelly/Signature-Herbal-Jelly
Hahaha, bingo! :D
y''-tan(x)y+2y=0
The other technique for solving it is change of independent variable
t=tan(x)
dt/dx=1+tan^2(x)
dt/dx = 1+t^2
dy/dx = dy/dt*dt/dx
dy/dx = (1+t^2)dy/dt
d^2/dx^2 = d/dx(dy/dx)
d^2/dx^2 = d/dt((1+t^2)dy/dt)(1+t^2)
d^2/dx^2 = (2t dy/dt + (1+t^2)d^2y/dt^2)(1+t^2)
(1+t^2)^2d^2y/dt^2+2t(1+t^2)dy/dt - t(1+t^2)dy/dt+2y=0
(1+t^2)^2d^2y/dt^2 + t(1+t^2)dy/dt + 2y = 0
Now it is easier to solve by series expansion
WTF!!!!
same
WTF!
hell man get camera right !
WTF
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