  Often a non-linear mechanical problem is formulated as a non-linear
differential equation. A new method is introduced to find out new solutions of
non-linear differential equations if one of the solutions of a given non-linear
differential equation is known. Using the known solution of the non-linear
differential equation, linear differential equations are set up. The solutions
of these linear differential equations are found using standard techniques.
Then the solutions of the linear differential equations are put into non-linear
differential equations and checked whether these solutions are also solutions
of the original non-linear differential equation. It is found that many
solutions of the linear differential equations are also solutions of the
original non-linear differential equation.
