New solutions for the elliptic Darboux equation are obtained as particular cases of constructed Heun's general equation. We consider two groups power series expansions and new in Gauss hypergeometric functions. The convergence one group is determined by means ratio tests infinite series, while other designed to solve problems which admit finite-series solutions. Actually, we envisage periodic q...

existence of periodic solutions for non-linear third order autonomous differential equation (o.d.e.) has not been investigated to as large an extent as non-linear second order. the popular poincare-bendixon theorem applicable to second order equation is not valid for third order equation (see [3]). this conclusion opens a way for further investigation.