Find the solution of the given initial value problem in explicit form: 19. sin(2x)dx + cos(3y)dy = 0, y(pi/2) = pi/3 Solution sin(2x)dx + cos(3y)dy = 0 As variables are separate integrate to find x and y -cos 2x/2 +sin3y/3 =C Or -3cos2x+2sin3y = C\' x=pi/2, y =pi/3 Substitute to get -3cospi+2sinpi = C\' = 3 ----------------------------- Hence solution is the implicit equation -3cos2x+2sin3y = 3.

1. Find the solution of the given initial value problem in explicit form:
19. sin(2x)dx + cos(3y)dy = 0, y(pi/2) = pi/3
Solution
sin(2x)dx + cos(3y)dy = 0
As variables are separate integrate to find x and y
-cos 2x/2 +sin3y/3 =C
Or -3cos2x+2sin3y = C'
x=pi/2, y =pi/3
Substitute to get
-3cospi+2sinpi = C' = 3
-----------------------------
Hence solution is the implicit equation
-3cos2x+2sin3y = 3