Question

dy/dx=x+y, y(0)=1

How do I solve for y(x)?

I know the answer is y(x)=2e^x-x-1, but I forgot how to do these kinds of problems again.

Answer 1

This is and ordinary differential equation with exact roots.

What I suggest to review these is to go to Barnes Noble, or any good bookstore, and purchase Schaum's Outline Series, Differential Equations, an excellent book and buy. Take a look.
There is an abridged version online
http://www.ebookmall.com/ebook/133885-ebook.htm
But, I would be wary of abridging a condensed study guide.

Good luck.

Answer 2

This is a first order linear differential equation and can be solved by the "integrating factor" method.

See http://www.sosmath.com/diffeq/first/lineareq/lineareq.html