Thread: (sinx) dy + ( y cosx - x sinx ) =0

1. (sinx) dy + ( y cosx - x sinx ) =0

the pic post is the solving using exact equation method , but
the author solve it using another method ( i typed below)

after rearranging , we have

dy/dx + y cotx = x

integrating factor = sin x

d/dx( ysinx) = ∫x sinx dx

so , finally , i have ysinx +xcosx - sinx = C

why not the final ans =
ysinx +xcosx - sinx + C = 0 ???

2. Re: (sinx) dy + ( y cosx - x sinx ) =0

$\displaystyle C$ is an arbitrary constant - any value for $\displaystyle C$ is valid. Instead of writing $\displaystyle C$ we might write $\displaystyle C_1=-C$ which is still an arbitrary constant, and then your result comes out exactly.