gdullard (November 30, 1999 at 12:00 am)

great teacher, better comedian haha 3:09

BannedLol4l (November 30, 1999 at 12:00 am)

@nejtilsvamp There may be cases (such as this one) where it is impossible to solve explicitly for y in terms of x, and so the implict solution is the best you can do. If Psi turned out to be, say, x+y, then you could have said y = C - x as the solution. But if you get y*sin(x) + x^2*e^y - y = C, you can't find an expression like y = f(x), because there is no way to isolate y.

4and6stringer (November 30, 1999 at 12:00 am)

@UniverselGamer A2. Yes. Integrate psi y then add f(x). Get the derivative wrt x. Equate it with psi x to get the value of f'(x) to get f(x).

4and6stringer (November 30, 1999 at 12:00 am)

@UniverselGamer A1. psi might have terms that 1.) have y 2.) have y plus constant or 3.) or just constants only (which is what we got) When deriving psi wrt x only, all of these are treated as constants, thus all having derivative of 0. To be safe, you always assume 1.) or 2.) or both is true, that's why you put f(y) instead of C. If f(y) ends up as a constant then you have no problem there.

UniverselGamer (November 30, 1999 at 12:00 am)

Q1. from "4:40" to "5:30", i don't understand why +C is replaced with f(y). And also i dont understand how when taking the partial derivative of f(y) will equal to 0 wrt x, if y is a constant wouldn't it still be f(y)? Q2. if we took the antiderivative of psi(y) would that "+C" be replaced by f(x)?

tam3ree (November 30, 1999 at 12:00 am)

Hey Sal, shouldn't you put "+C" at the end of psi at 6:40 ? Or is it included in f(y) ? Thank you!

Jawshooah (November 30, 1999 at 12:00 am)

I'm always astounded at how much more fluidly and coherently Sal is able to explain mathematical and scientific concepts than my professors and TAs. You, sir, are awesome :D

shmittythepirate (November 30, 1999 at 12:00 am)

@manny34711 yeah...

manny34711 (November 30, 1999 at 12:00 am)

shouldnt f'(y)=-1 instead of 1?

Marinecorps1812 (November 30, 1999 at 12:00 am)

@nejtilsvampe I know you asked this a long time ago, but Psi is an intermediate step to solving the Differential Equation in terms of x and y. Yes, it's preferred to solve for y explicitly, but sometimes it's hard so an implicit solution is okay. For example: Y = X + 1 is the same as 1 = Y - X