1) If y'' + E y = 0, and y(0)=0 and y(1)=0.  Find the general solution to this ODE (when E is a constant).  Enforce the Boundary Conditions.  What values of E allow for a non-zero solution to this ODE.

2) y' = -(x^2-y)/(y^2-x)

3) y'' + y/(4 x^2) = 0

4.) x^2  y'' - 2xy' + (x^2+2)y=0.   given x cos x is a solution

5.)  d/dx ( y' + x y) = 0   [See the similar homework problem]