1. The problem statement, all variables and given/known data x²y'' + (x² - 2)y = 0 2. Relevant equations N/A 3. The attempt at a solution I divided through by x² to get the equation in standard form. Then I plugged in the power series representation for y and y'' into the equation and got to this point... http://www.meteo.psu.edu/~jmg498/equ.png [Broken] Now, I know that I want the powers on x to be the same. But before I do an index shift, I'm not really sure how to handle the (x² - 2)/x² in front of the sum in the second term. If it were just an x, then I would be able to strip one element off the index. But since it's not just an x or power of x, I'm not really sure how to handle it. Thanks for any hints!