Find the first six non-zero terms of the power series solution at

x = 0 of the following IVP.

So far I have:

supposing that is the power series solution I have solved for .

and from I have solved for

Using

I have got first and second derivative of the sum and have plugged into the original equation and got:

But now I get confused as to what to do next to have the same power of x as what my sum begins with.

Can anyone tell me how I could break down my sums to solve for my 6 terms.

Thank you!!!