North West University,

Private Bag X 2046,

Mmabatho 2735,

SOUTH AFRICA

E-mail: khaliquecm@uniwest.ac.za

**Symmetry and homotopy analysis of third-order ODEs**

**Abstract:**

We obtain the solution of the Chazy equation using homotopy analysis
and compare it with the solution obtained via symmetry analysis. The solution
of the Chazy equation is then used to construct an approximate solution
of a third-order ODE which arises in the flow of radial stretching of a
sheet. This solution of the third-order ODE is compared with that obtained
using homotopy analysis. We also use the Airy functions to construct such
solutions and compare the results.