Suppose and are different solutions of the same inhomogeneous linear equation . Find, in terms of and , a family of solutions of this equation depending on an arbitrary constant.

I am not sure how to start.

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- Dec 29th 2010, 04:40 PMdwsmithu_1 and u_2 are two different sol. of Au=f
Suppose and are different solutions of the same inhomogeneous linear equation . Find, in terms of and , a family of solutions of this equation depending on an arbitrary constant.

I am not sure how to start. - Dec 29th 2010, 05:40 PMProve It
Is a constant? Are functions of ?

- Dec 29th 2010, 05:42 PMpickslides
Hi dw, this seems quite general and probably the reason you can't get started.

Are you are looking for ?

Take a look at posts #8,11,12,13. See if anything you are studying is firmilar.

http://www.mathhelpforum.com/math-he...ial-38182.html - Dec 29th 2010, 05:52 PMdwsmith
To Prove it, u is usually a function of x and y i.e. u(x,y). I have no idea what f is but I am thinking it is a function of x and y, f(x,y). A is a linear operator.

To pickslides, I am not sure what I am looking for.

This is the introduction section to Linear Operators.