How to solve these simple diff eq's

1. dy/dx = (cosy)^2
2. dy/dx = e^(x-y)
3. dy/dx = (cosx)(e^(y+sinx))

dy/dx = cos(y)^2
dy/cos(y)^2 = dx
sec(y)^2 * dy = dx
tan(y) = x + C
y = arctan(x + C)


dy/dx = e^(x - y)
dy/dx = e^(x) / e^(y)
e^(y) * dy = e^(x) * dx
e^(y) = e^(x) + C
y = ln(e^(x) + C)



dy/dx = cos(x) * e^(y + sin(x))
dy/dx = cos(x) * e^(y) * e^(sin(x))
dy/e^(y) = e^(sin(x)) * cos(x) * dx
e^(-y) * dy = e^(sin(x)) * cos(x) * dx

u = sin(x)
du = cos(x) * dx

e^(-y) * dy = e^(u) * du
-e^(-y) = e^(u) + C
e^(-y) = C - e^(u)
e^(-y) = C - e^(sin(x))
-y = ln(C - e^(sin(x))
y = -ln(C - e^(sin(x))

1/
tany = x + c
2/
e^y = e^x + C
3/
e^-y dy = cosx e^sinx dx ---> -e^-y = e^sinx + C