I have a whole set of differential equations that I have to solve, so I am going to list them all, but if someone could just help me with one or two of them, I should be able to solve the rest??? Thanks.
1. xy' = y + 1
2. y" + y' - 2y = sin x + e^x
3. y" + y = sin x, y(0) = 1, y'(0) = 0
4. y"' - y' = xe^x
5. (1 - x^2)y" - 2xy' + 42y = 0
(number 4 looks different than the others, so maybe if someone could help me with that one and one other I would be able to solve the rest. Thank you very much!)