dy/dx=3cos(x)y,
dy/y=3cos(x)dx,
ln(y)=3sin(x)+C, where C is a constant,
y=e^(3sin(x)+C) which is always positive, so y cannot be -2.
Perhaps you meant dy/dx=3cos(x)/y?
If so:
ydy=3cos(x)dx,
Integrating:
y²/2=3sin(x)+C.
Plug in x=π/2 and y=-2:
2=3+C, C=-1, y²/2=3sin(x)-1.
This can be written: y²=6sin(x)-2.