Find kernel function of integral equation

Is it possible to find a kernel function of integral (symbolic solution).

Somrthing like this:

$ \sin(x) = \integral (knowFunc(x) + unknownFunc(x) dx) $

Whats code implement this?

[Walter Roberson]

There are a number of different transforms each leading to a different kernel, so this question feels a bit vague.

[Vladimir]

Is it inpossible to get common solution? Or a few samples of common solution?

If this is inpossible, can matlab solve this integral:

$ \sin(x) = \integral_0^t (knowFunc(x) + unknownFunc(x) dx) $

[Walter Roberson]

No, that cannot be solved. The left hand side does not involve t, but the right hand side involves t.

Even if you were to convert to

\integral_0^x(knowFunc(t) + unknownFunc(t) dt)

then the question is still too vague to be meaningful. What are the restrictions on unknownFunc ? Does it have to consist of terms whose coefficients are not present anywhere in the Online Encyclopedia of Integer Sequences ("unknown" == "uncatalogued" ??)

[Torsten]

Something like

unknown function = -known function + sin(x)

?

[Vladimir]

Thank you a lot for your answers, but a question was not about how to solve example, but about how to solve it with matlab. The example was an abstract, and I will try to explain it in other way.

I can't introduce in matlab a integral from unknown function. \integral y(x)*dx was solved immidiatly but not correct. Matlab undestand 'y' as a free variable, not a function of 'x', and solve it in 'y*x'. Is there any way to solve this type equation?

I try to give you another example: \integral(y(x)) = 2x I know the solution, but whats code to solve it in matlsb?

[Walter Roberson]

>> diff(int(y,x)==2*x)
ans(x) =
y(x) == 2

?

[Vladimir]

Thanks, but I mean not differentiate a equation, but solve it. If I do in in this way:

>> z = sin(x) == int(y, x)

z =

sin(x) == x*y

it give me a wrong answer.

[Walter Roberson]

syms y(x)
Z = sin(x) == int(y, x)
diff(Z, x)

You will get a cosine solution that is the correct value for y(x)

[Vladimir]

Exacly what I need, thanks a lot. One more question, can I solve this equation with command 'solve' or 'dsolve'?

[Walter Roberson]

No, solve and dsolve do not understand solving when int() are present.