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Let $\bbK$ be an ordinary differential field with derivation $\partial$. Let$\cP$ be a system of $n$ linear differential polynomial parametric equations in$n-1$ differential parameters with implicit ideal $\id$. Given a nonzero lineardifferential polynomial $A$ in $\id$ we give necessary and sufficientconditions on $A$ for $\cP$ to be $n-1$ dimensional. We prove the existence ofa linear perturbation $\cP_{\phi}$ of $\cP$ so that the linear completedifferential resultant $\dcres_{\phi}$ associated to $\cP_{\phi}$ is nonzero. Anonzero linear differential polynomial in $\id$ is obtained from the lowestdegree term of $\dcres_{\phi}$ and used to provide an implicitization algorithmfor $\cP$.

A perturbed differential resultant based implicitization algorithm for linear DPPEs