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Assuming knowledge of homogeneous ODEs and nonhomogeneous ODEs that can be made homogeneous (eg, y'-y=x), how does one solve those that cannot be made homogeneous (eg, y'-y=cosx, y''-xy'+y=0, cos(y'')+sin(y')=0)?

EDIT: Maybe "made homogeneous" is the wrong way to put it... By being able to be "made homogeneous," I mean it is possible to differentiate the right hand side to 0 so as to find the general form of the particular solution.

EDIT: Maybe "made homogeneous" is the wrong way to put it... By being able to be "made homogeneous," I mean it is possible to differentiate the right hand side to 0 so as to find the general form of the particular solution.

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