Help with Differential Equations homework-Separable Functions

I'm not one to ask for answers to my homework, but some of these problems I just don't know whether I'm missing something, because it's basic separable equations. I don't think it's that hard but any help would be appreciated, thank you.
Solve the equations. Find an explicit solution if possible:
1) (1+x)y' + y = cosx
2) y' = ye^x - 2e^x + y - 2
3) y' = x/(2y-6)
4) y' = sec^2(y)/(1+x^2)
5) y' = y + 2x*e^(2x)
6) sinx(dy/dx) + y*cosx = 2xsinx
Some of them I don't think can be solved explicitly like 3 and 4, but I'm not sure.
Thank you very much for your help!

1. A slight trick here, notice that d/dx [(1+x)y] = y + (1+x)y' which is the LHS.
d/dx [(1+x)y] = cosx
y = (cosx + C) / (1 + x)

2. y' - y(e^x + 1) = -2(e^x + 1)
Multiply both sides by the integrating factor e^(-e^x - x):
d/dx [(e^(-e^x - x))y] = 2(-e^x - 1)(e^(-e^x - x))
Conveniently the RHS integrates to e^(-e^x - x) so this is easy to solve.

3. This can be separated to (2y - 6)dy = x dx which can easily be integrated.

4. Also separable and easily integrated to trig functions explicitly.

5. Multiply by e^x: (e^x)y' - (e^x)y = 2x*e^(3x) = d/dx(e^x * y)
The RHS can be integrated using integration by parts.

6. The LHS is just d/dx [ysinx]. The RHS can be solved by parts.