W8S63
Let $k_1, k_2$ be constants and consider the ODE $y'' - (k_1 + k_2)y + k_1k_2y = f(x)$, whose auxiliary equation has roots $k_1 = -2$ and $k_2 = -2$. Suppose
$f(x) = 4e^{2x}$.
Choose a particular integral $y_p$ from those below.
Select one:
$\circ$ a. $y_p = ae^{2x}$ for some constant $a$ to be found.
$\circ$ b. $y_p = ax^2e^{2x}$ for some constant $a$ to be found.
$\circ$ c. $y_p = axe^{2x}$ for some constant $a$ to be found.
$\circ$ d. $y_p = e^{2x}(a_2x^2 + a_1x + a_0)$ for any constants $a_0, a_1, a_2$.
$\circ$ e. $y_p = e^{2x}(a\sin(x) + b\cos(x))$ for any constants $a, b$.
