- #1

manenbu

- 103

- 0

## Homework Statement

Solve:

[itex](x^2-1)y'' + 4xy' + 2y = 6x[/itex], given that [itex]y_1=\frac{1}{x-1}[/itex] and [itex]y_2=\frac{1}{x+1}[/itex].

## Homework Equations

## The Attempt at a Solution

Since both solutions are given, the solution to the homogenous system is:

[tex]y_h=C_1\frac{1}{x-1} + C_2\frac{1}{x+1}[/tex]

And the solution to the original equation would be:

[tex]y=C_1(x)\frac{1}{x-1} + C_2(x)\frac{1}{x+1}[/tex]

To solve I use this system of equations:

[tex]C_1'(x)\frac{1}{x-1} + C_2'(x)\frac{1}{x+1} = 0[/tex]

[tex]-C_1'(x)\frac{1}{(x-1)^2} - C_2'(x)\frac{1}{(x+1)^2} = 6x[/tex]

Somehow, all of this should end up being: [itex]y=\frac{C_1}{x-1} + \frac{C_2}{x+1} + x[/itex], according to the answers, but I just can't get there. Was there anything wrong in the systems of equations? Or is it me solving for the constants (I didn't write it here)?