Variation of Parameters
Summary
Our quest on finding a particular solution of $$ x^{\prime \prime}(t)+p(t) x^{\prime}(t)+q(t) x(t)=f(t) $$ continues. Earlier, we used the Method of Undetermined Coefficients to do that. That method had two restrictions
- the coefficients $p(t)$ and $q(t)$ had to be constants (the ODE is constant-coefficient),
- the forcing $f(t)$ had to be from special families of functions such as exponentials, trigonometric, polynomials.
With the Variation of Parameters, we will lift these restrictions.