This problem has been bugging me and I can't seem to figure it out: y'' = e^y where y(0)= 0 and y'(0)= -1 I'm supposed to get the first 6 nonzero terms I know the form is: y(x) = y(0) + y'(0)x/1! + y''(0)x^2/2! + y'''(0)x^3/3! +...... and I know the first two terms are y(x) = 0 - x +..... But whats troubling is the e^y. How would I go about getting the y''(0) term. I tried a subsitution of u = y', but the integrals gets very messy. I'm thinking there is either a typo in the book or there is a simpler way to get the answer. All I need is an example of how to get the next term. I can figure out the rest.