I'm currently teaching myself some differential equations by watching the MIT OCW series on the topic. In This video, at 21:50mins, the lecturer calculates the following derivatives:
My simple question is, how he came to the second one. Is this a "total derivative" and why is it required? If I try to calculate the total derivative of y', I get:
$y''=(2x-1)dx+(1-2y)dy=2x dx - 2y dy$
I'm pretty sure that I made a silly mistake. Thanks for your help!