The idea of variation of parameters is to seek the solution to

in the form

whereby

is a fundamental matrix.

Note that the constant vector

**c** of coefficients is replaced by an unknown function

**v**(t).

What is the equation for our unknown function

**v**(t) you ask?

It is fairly straight forward to derive:

.

*IMPORTANT:* You must make sure that

exists in order to solve for

**v** !!!! (not factorial

)

Finally, using integration, we have:

I'll now rewrite the original problem in latex so it is more palatable to the eye:

Find the general solution of

, whereby

.

Does this help?