Verify that the indicated family of functions is a solution ofthe given differential equation. Assume an appropriate intervalI of definition for each solution.
d^2y/ dx^2 − 6 dy/dx + 9y = 0;    y =c1e3x +c2xe3x  When y =c1e3x + c2xe3x,
Thus, in terms of x,
| d^2y/dx^2− 6 dy/dx + 9y | = | + 9(c1e3x +c2xe3x) |
| = | Â Â . |
2) In this problem, y = c1ex +c2e−x is a two-parameter family of solutionsof the second-order DE
y'' − y = 0. Find a solution of the second-order IVP consistingof this differential equation and the given initial conditions.
y(−1) = 7,    y'(−1) = −7
y =
