Do you mean expressing the solution in an orthonormal base ? If yes, this is the starting point of the theory of orthogonal polynomials in L2. For instance, in order to solve the ODE for prolate spheroidal functions, you decompose the corresponding solns into Legendre polynomials, which are solns of a related (but simpler) ODE.

Thanks for the nice explanation @David W. Pravica.

Dear @Soh,  Gram-Schmidt Orthogonalization Process is a process that is used to find a set of orthogonal polynomials on a closed interval [a,b] with respect to a weight function w(x); thereafter, these polynomials can be used in the solution of an ODE or the least-squares approximation or any other application. In solving ODEs, the solution is written in terms of the orthogonal polynomials, substituted in the ODE, and thereafter using the orthogonality property to find the coefficients of the solution as explained by dear @David.