Hello, everyone. I am new here. This is just high school Calculus. Don't laugh at me .

Can someone tell me how these problems work? I even looked at the answers (yes, I *am* allowed to do that) but I can't work them backwards. The first one is this:

dy/dx = y+2

And this is what I did:

dy = (y+2) dx

y = Ce^x + 2x

Now the answer is y = Ce^x - 2 .

And the second one: y' = y√x

And last: (1 + x^2)y' = 2xy