- #1

s3a

- 818

- 8

## Homework Statement

The problem is attached as TheProblemAndSolution.png, and everything is typewritten, so it should be easily legible (but you will likely need to zoom into read the text since the image's height is significantly larger than its width).

## Homework Equations

Differential operator method.

Wronskian.

Variation of parameters.

Integration.

## The Attempt at a Solution

__What I understand__:

1. I understand what an Euler equation is.

2. The Cramer's rule part.

3. The Wronskian part.

4. The variation of parameters part.

5. The integrating part.

6. The part about forming the general solution given the previous data.

__What I don't understand__:

1. Why is x^4 ln x in the question? Using WolframAlpha.com to confirm, the general solution presented at the end of the solution of this problem is that of x^2 y'' – 4x y' + 6y = x^4 sin x and not x^2 y'' – 4x y' + 6y = x^4 ln x.

2. I don't get the phi(t) = y(e^t) part.

3. I don't get the [D(D – 1) – 4D + 6] phi(t) = [(D – 3)(D – 2)] phi(t) = 0 part.

4. I don't get the y_1(x) = |x|^3 and y_2(x) = |x|^2 part.

Any input helping me fully understand this problem would be GREATLY appreciated!