A linear differential equation of second or higher order have more than $1$ solutions of $y (y1, y2,$ etc.). Hence a common solution is obtained by assuming $y = c1y1 + c2y2+.....$ 
Now my questions are:

1. How are linear differential equations formed from general algebraic expressions?
2. Why is it that a linear differential equation of second or higher order contain more than one solution of y that satisfy them?