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# Solutions to Differential Equations Exercises

### Example 1

Determine whether y = ex is a solution to the d.e.

y' + y" = 2y.

### Example 2

Determine whether y = xex is a solution to the d.e.

y' = xy.

### Example 3

Determine whether P = e-t is a solution to the d.e.

### Example 4

Determine whether y = x2 is a solution to the d.e.

### Example 5

Determine whether y = xn is a solution to the d.e.

x2y" + ny = n2y.

### Example 6

Show that y = 5x2 + 2 is a solution to the d.e.

### Example 7

Show that y = 5x2 is not a solution to the d.e.

### Example 8

Show that f (x) = sin x is a solution to the d.e.

f (2)(x) + f (x) = 0.

### Example 9

Show that f (x) = exsin x is a solution to the d.e.

2f '(x) – 2f (x) = f ''(x).

### Example 10

Show that y = ln x is a solution to the d.e.

ey = x2y'.