Example 4.  Neither of the solutions in 2 and 3 solve the given boundary values.  Graph them to verify this.
However, you should be able to "see the initial conditions"  u(1) = 1, u'(1) = 0  and  v(1) = 0, v'(1) = 1. for u and v, respectively.

Solution 4.

(c) John H. Mathews 2004