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In this work for the one class first order model and non model integro-differential equation with right and left singular point in the kernel, obtained integral representation manifold solution by two arbitrary constants. It was built the analogue of theorems of Fredgolm for some classes integro-differential equation. Moreover similar results are received for the corresponding conjugate integro-differential equations. The method of solving this problem can be used for the solving of higher order model and non-model integro-differential equations with singular coefficients.