Solve Series Solutions Homework Equations

[WTBash]

Homework Statement

1. Using series solution to solve dy/dx - y(x) = x where y(0) = -1. [y(x) = Σ ak x^k from 0 to infinity.
2 Find c0 and c1 in y(x) = c0 e^αx + c1 e^-αx so that y(x) = a0 cosh(αx) +(a1/α) sinh (αx)
3. Find the 2 independent solutions of x d2y/dx2 + 2 dy/dx +xy = 0 using the frobenius solution with r = 0, -1

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

You seem to have left out "The attempt at a solution". Certainly no deep thinking is required. Find the first derivative of $y= \sum_0^\infty a_k x^k$ and put those two series into dy/dx- y= x.