- #1

deadsupra

- 13

- 0

We used M and N for ∂f/∂x and ∂f/∂y, respectively. (it is completely arbitrary)

She taught us that we must integrate either M or N and the constant of integration will be g(x).

To find g(x), we must integrate g(x) prime. and g(x) prime is simply the other M or N not already integrated.

The way I see it, M and N will be integrated either way. So is it not possible to simply integrate both M and N and match the similar values.

For example:

Given the exact equation: (2xy)dx+(x^2)dy=0

Her solution:

∂f/∂x = 2xy

and

∂f/∂y = x^2

(first one) f = (x^2)y + g(x)

with g(x) = ∫x^2 dy

therefore: f = (x^2)y + c (a constant)

My solution (line by line):

∂f/∂x = 2xy

∂f/∂y= x^2

(they were side by side)

(next line)

f(x,y)= (x^2)y + c(y)

f(x,y)= (x^2)y + c(x)

(also side by side on same line)

final answer: (x^2)y + c

(I rewrote the constant as c sub 1)

Same answer. Same idea in the process (integrate both M and N). Same solution. Different method.

This was a test question. She deducted points because she said I didn't show work. She also wrote that c(x)=c(y) is false, which after I talked to her she admitted it was correct but stated that "there are many problems that you will run into trouble with if you don't do it my way." I stated that she does integrate both M and N regardless of which method, she said I was wrong.

She said she couldn't give me a specific example because other students were waiting to ask questions. I will make an appointment with her later this week to take her up on that offer.

I noticed this method during lecture when she was lecturing ever so slowly to allow people to catch up and learn. I used this method of matching the same function integrated with different variables in my LONG, weekend-killer homework and no answer was wrong because of the process.

P.S. Sorry for sounding like a butt, but I believe I am correct and I am, for the most part, a humble person. not as obnoxious or rebellious as this post seems to look like.