Chapter 9.1, Problem 59E

In Problems 59 and 60, use window dimensions Xmin = – 5, Xmax = 5, Ymin = –5, and Ymax = 5.

59.    Given that $y=x+C{e}^{-x}$ is the general solution of the differential equation $y^{\prime }+y=1+x$:

(A)    In the same viewing window, graph the particular solutions obtained by letting C = 0, 1, 2, and 3.

(B)    What do the graphs of the solutions for C > 0 have in common?

(C)    In the same viewing window, graph the particular solutions obtained by letting C = 0, – 1, –2, and –3.

(D)    What do the graphs of the solutions for C < 0 have in common?