Hello, I'm currently talking Calculus 2, and the last chapter we cover in this course talks about solving D.E. using series. As a reference my professor uses the Stewart Calculus book, and in particular, the problems I'm struggling with are from chapter 17.4 - Series Solutions. Below I posted two of the assigned practice questions, plus some of my thoughts on how to approach them. Thanks for any help/advice!
Find two independent series solutions for:
1) y" - 2xy' - 4y = 0
2) y" - (x^2)y' - 3xy =0
For both problem I set the general power series form equal to y. Then I would take the 1st and 2nd derivative to substitute it back into the formula above, resulting in a difference of summations. By changing the starting point of the middle term I could combine the 2nd and 3rd summation and solve for the constant Cn+2 (found by setting n=0 for the first summation). After this point I don't really know how to go about finding 2 separate series to fit into the general solution form for D.E.
Again, thank you for any tips!
Find two independent series solutions for:
1) y" - 2xy' - 4y = 0
2) y" - (x^2)y' - 3xy =0
For both problem I set the general power series form equal to y. Then I would take the 1st and 2nd derivative to substitute it back into the formula above, resulting in a difference of summations. By changing the starting point of the middle term I could combine the 2nd and 3rd summation and solve for the constant Cn+2 (found by setting n=0 for the first summation). After this point I don't really know how to go about finding 2 separate series to fit into the general solution form for D.E.
Again, thank you for any tips!