‎For a given subspace as a solution space of a linear ODE‎, ‎we define a special linear parametric group action and prolong it to the jet bundle‎. ‎We determine these group parameters by moving frame method and prove that these group parameters are the first integrals of the given ODE‎. ‎These first integrals are used to construct the general form of operators which preserve given subspace invariant‎. Manuscript profile