Problem 1 version R-Z
Add (x/16)e^(-4x) to the expression for y(x).
PDF source on web has been fixed.

Problem 2 version A-D
Change the DE right side to x^3 + e^x - cos(3x)
PDF source on web has been fixed.

Problem 2 version L-Q
Sign typo.
Change y''' + y''  to  y''' - y''.