It’s 2 days before the AP Calculus test and I need a question answered:
You integrate a differential equation and get 2y = x + C. Does that equal y = .5x + C or y = .5x + .5C? My book says it’s the former because .5*constant = another constant, but I believe it is the latter. Here’s why.
Say that they give you the point (1, 2) to solve for C:
2y = x + C
2*2 = 1 + C
3 = C
Confirmation:
y = .5x + .5C
2 = .51 + .5C
2 - .5 = .5C
1.52 = C
3 = C
But using the books method:
y = .5x + C
2 = .5*1 + C
1.5 = C
