Chapter 7.2, Problem 1E

a)

To determine

Show that the function $y=e^{-x}$ is a solution of the differential equation $2y^{\prime }+3y=e^{-x}$.

b)

To determine

Show that the function $y=e^{-x}+e^{-\left(\frac{3}{2}\right)x}$ is a solution of the differential equation $2y^{\prime }+3y=e^{-x}$.

c)

To determine

Show that the function $y=e^{-x}+C{e}^{-\left(\frac{3}{2}\right)x}$ is a solution of the differential equation $2y^{\prime }+3y=e^{-x}$.