<aside> 📎 For the nonhomogenous linear differential equation, $y’’+y’ + y != 0$

</aside>

Method of Undetermined Coefficients

1. Solve the complementary equation and write down the general solution
2. Based on the form of $r(x)$, make an inital guess for $y_p(x)$
3. Check whether any term in the guess for $y_p(x)$ is a solution to the complementary equation
   1. If so, multiply the guess by $x$
   2. Repeat this step until there are no terms in $y_p(x)$ that solve the complementary equation
4. Subsitude $y_p(x)$ into the differential equation and equate like terms to find values for the unknown coefficients in $y_p(x)$
5. Add the general solution to the complementary equation and the particular solution you just found to obtain the general solution to the nonhomogenous equation