1. The problem statement, all variables and given/known data Find the Taylor expansion y(x) satisfying: y'(x) = 1 - xy 2. Relevant equations 3. The attempt at a solution So I need expressions for y''(x), y'''(x), ...etc I can find y''(x)=-y-xy' by differentiating implicitly. By setting y'(x)=z, then dz/dx = δz/δx+(δz/δy)(dy/dx) However when I use the same method to try and find y'''(x) I have problems: - partial differential of y'(x) ? - is the (dy/dx) from the implicit formula still dy/dx or the second differential? [Ans: -2y'-xy''] Please tell me the technique, or give me a reference, that is used to find y'''(x) in this example? Thanks!