Originally Posted by

**Jameson** I don't follow this completely, but the general idea is straightforward enough I think.

Do you see that CaptainBlack just wrote a general Taylor expansion for y(x)? Then he took the second derivative for a few terms. You're D.E. says that yy''=x, so he multiplied these two series expansions. They are infinite expansions but you only need x^5 as your highest term, and when you multiply the LHS of course the powers will add so you really do not need that many terms.

Does that part make sense? Writing y and y'' in terms of a general Taylor expansion.

The only part I'm not seeing is when CB says after expanding the product on the LHS equating powers to get coefficients. Equating the product with what? Just x?