Many quantum algorithms for differential equations dilate non-unitary dynamics using a continuous auxiliary variable, which is normally discretized onto a costly qubit register. I will show that continuous-variable oscillator modes can instead carry this variable natively. For linear systems, we encode the LCHS kernel directly in an oscillator’s state through preparation and postselection, with provable bounds on the resulting truncation, Trotter, and sampling costs. For nonlinear ODEs, we linearize via the Fokker–Planck equation and couple the discretized density to a qumode carrying the full Schrodingerisation continuum, yielding an oracle-free circuit synthesis with cost polynomial in dimension and polylogarithmic in grid size. Both results point to hybrid oscillator-qubit architectures as a practical, resource-efficient alternative to fully discretized ancilla registers.