Math Bits - Series Solutions

Students should have experience with big sigma notation, especially reindexing a series and writing out several terms to see trends.

1. (Series Solutions One)

   1. Use the power series method to find the first six terms in each of two independent solutions to this differential equation.

   2. Solve this differential equation using a different method and show that your answers are the same as part a.

2. (Series Solutions Two)

   1. Use a power series expanded about $x = 0$ to find the first six terms in each of two independent solutions to this differential equation.

   2. For what values of $x$ do each of your power series solutions converge?

   3. Suppose you were to subtract one of your two solutions from the other solution. Is the resulting function still a solution to the original differential equation? Explain.