- #1

ABearon

- 5

- 1

- TL;DR Summary
- are c1 and c2 just random coefficients

I'm having a hard time grasping the concept of reducing the two recursive relations at the end of the frobenius method.

For example, 2xy''+y'+y=0

after going through all the math i get

y1(x) = C1[1-x+1/6*x^2-1/90*x^3+...]

y2(x) = C2x^1/2[1-1/3*x+1/30*x^2-1/630*x^3+...]

I know those are right, and I know we solve for what's inside the bracket by taking a C0 out. I'm just trying to clarify that, since c0 is different for each term and since it is arbitrary we can just write c1 for y1 and c2 for y2. I want to make sure this is where the c1 and c2 come from and not from trying to take out a c1 in the y1 brackets and c2 in the y2 brackets.

For example, 2xy''+y'+y=0

after going through all the math i get

y1(x) = C1[1-x+1/6*x^2-1/90*x^3+...]

y2(x) = C2x^1/2[1-1/3*x+1/30*x^2-1/630*x^3+...]

I know those are right, and I know we solve for what's inside the bracket by taking a C0 out. I'm just trying to clarify that, since c0 is different for each term and since it is arbitrary we can just write c1 for y1 and c2 for y2. I want to make sure this is where the c1 and c2 come from and not from trying to take out a c1 in the y1 brackets and c2 in the y2 brackets.