  In this work, we obtain third order linear differential equation for
stationary distributions of run-and-tumble particles in two-dimensions in a
harmonic trap. The equation represents the condition $j = 0$ where $j$ is a
flux and is obtained from inference, using different known results in the
limiting conditions. Since the analogous equation for passive Brownian
particles is first order, a second and third order term must be a feature of
active motion. In addition to formulating the problem as third order equation,
we obtain solutions in the form of convolution of two distributions, the
Gaussian distribution due to thermal fluctuations, and the beta distribution
due to active motion at zero temperature. The convolution form of the solution
indicates that the two random processes are independent and the total
distribution is the sum of those two processes.
