This problem has been bugging me and I can't seem to figure it out:(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Taylor Series

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