How far does your instructor want the Taylor series taken?
I have to step out for a little school shopping. I will be back as soon as I can. Hopefully you will have an answer for me by then.
Ok, after working on these for a while, I should ask how much detail you need to see. There is a *lot* of typing for me to show all the work.
The next to last question includes a symbol that is not showing properly.
"dy/dx = y³ sin x" and then "y(0)=0"
As written that problem has no solution. Please resend that problem.