Question

slove (xysinxy+cosxy)ydx+(xysinxy-cosxy)xdy=0​

Answer 1

Answer:

Explanation:

Dear student

Starting with ydx+xdy = d(xy),

(xy) sin(xy) d(xy) + cos(xy) (y dx - x dy) = 0,

dividing by (xy) cos(xy):

sin(xy)/cos(xy) d(xy) + dx/x - dy/y = 0,

d(-cos(xy))/cos(xy) + d(log|x| - log|y|) = 0,

-log |cos(xy)| + log|x| - log|y| = -log|C|,

Cx = y cos(xy).

x = 0 is a solution, too.