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I'm having trouble solving an integral equation. It appears to me to be a homogenous fredholm equation of the second kind. However, I'm being told that this can't be a fredholm equation, because it is non-linear. Could someone help me in trying to figure out how to classify an integral equation as linear or non-linear. Also, I'll post the equation I need to solve below, and it would be great if anyone could also give me some tips on how to try and solve it. Thank you to all who reply.

The equation is

$\phi(x) = (x^2 - x)\int\limits_0^1 \mathrm{d}y \frac{\phi(y)}{(y-x)^2}$

Also, is this by chance related to an eigenvalue problem? I know that might sound like a strange question, but I've seen some people treating these as eigenvalue equations.

By the way, I want to solve the equation for $\phi(x)$

2 added 58 characters in body

I'm having trouble solving an integral equation. It appears to me to be a homogenous fredholm equation of the second kind. However, I'm being told that this can't be a fredholm equation, because it is non-linear. Could someone help me in trying to figure out how to classify an integral equation as linear or non-linear. Also, I'll post the equation I need to solve below, and it would be great if anyone could also give me some tips on how to try and solve it. Thank you to all who reply.

The equation is

$\phi(x) = (x^2 - x)\int\limits_0^1 \mathrm{d}y \frac{\phi(y)}{(y-x)^2}$

Also, is this by chance related to an eigenvalue problem?

By the way, I want to solve the equation for $\phi(x)$

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# linear versus non-linear integral equations

I'm having trouble solving an integral equation. It appears to me to be a homogenous fredholm equation of the second kind. However, I'm being told that this can't be a fredholm equation, because it is non-linear. Could someone help me in trying to figure out how to classify an integral equation as linear or non-linear. Also, I'll post the equation I need to solve below, and it would be great if anyone could also give me some tips on how to try and solve it. Thank you to all who reply.

The equation is

$\phi(x) = (x^2 - x)\int\limits_0^1 \mathrm{d}y \frac{\phi(y)}{(y-x)^2}$

Also, is this by chance related to an eigenvalue problem?