D.E. Boundary Value Problem: Finished the work but it might be wrong

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Jeff12341234
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I get a different answer from my classmates. Where did I go wrong?

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First of all, this is not a boundary value problem. This an initial value problem.

Second, the expression you got for y'' is wrong.
 


if y" is wrong, then why does everything else check out? I double-checked it with my Ti-nSpire CAS and with Wolfram Alpha
 


I am sorry, I did not realize that you changed the order of terms in y''. It is correct. And I do not see any error in what follows.