Question

x'= y + 1/sint,

y'= -x,

Find a general solution of system using variation of parameters

Answer 1

Let us consider the matrix  , The eigenvalues of this matrix are .

Let us find the eigenvector for one root +i,

gives us .   .

Then the general solution is

Consider .

and also consider

Using the variation of parameters, the particular solution is

General solution is

.