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.