Question

Can anyone explain this for me? how did the equation (the left one) become like this after integral
x^2 dy + 2yx dx = sin3x dx
after integral
yx^2 = -cos3x/3 + c

Answer 1

product rule

Answer 2

reverse product rule

Answer 3

\((x^2y' + 2x y) = (x^2y)'\)

Answer 4

if you divide both sides by dx , you'll get
x^2 dy/dx + 2yx = sin3x

on the left side, it's just
d/dx (y x^2)

Answer 5

by FTC, \( \int (x^2y)' \) spits out \(x^2y\)

Answer 6

thank you guys

Answer 7

np :)