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Given smooth $f$. What is the solution $g$ of

$$ \lambda g''(x)=f(x)g(x) $$

where $\lambda>0$?

or more generally, given also $h$:

$$ \lambda g''(x)=f(x)g(x)-h(x)g'(x) $$

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you're right. since questions cannot be deleted here, I'll change it to another one I have. –  Troy McClure Jan 9 '13 at 16:45
    
@Troy I believe this is considered a bad form. You can delete a question by clicking delete under it. –  user53153 Jan 9 '13 at 16:55
    
somehow i dont have delete here like in other stackexchange, i also cannot vote here.. they have some bug –  Troy McClure Jan 9 '13 at 16:59
    
@Troy: your user is listed as "unregistered" here, and doesn't appear to be linked to other stackexchange sites except for StackOverflow. As an unregistered user, you cannot vote or delete. But I wonder if you have another SE account with different log-in credentials that somehow got split from this one? –  Willie Wong Jan 9 '13 at 17:03
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1 Answer 1

up vote 1 down vote accepted

There is no general method for solving such equations. For example, the solutions of the innocent-looking equation $$g''(x) = xg(x) \tag{1}$$ are Airy functions. What are Airy functions, one might ask? Well, they are defined as solutions of (1).

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