Chapter 1.8, Problem 20E

Consider the nonhomogeneous linear equation $\frac{dy}{dt}+2y=3t^2+2t-1$ .
In order to find the general solution, we must guess a particular solution $y_p\left(t\right)$ . Sincethe right-hand side is a quadratic polynomial, it is reasonable to guess a quadratic for $y_p\left(t\right)$ , so let $y_p\left(t\right)=a{t}^2+bt+c$ ,where a. b. and c are constants. Determine values for these constants so that $y_p\left(t\right)$ is a solution.