# Differential Equations and Their Solutions Exercises

### Example 1

Determine if the equation is a differential equation.

*f* ^{(2)}(*x*) + *f* (*x*) = 7*x*

### Example 2

Determine if the equation is a differential equation.

### Example 3

Determine if the equation is a differential equation.

*x*^{2} + *f* ^{2}(*x*) = 0

### Example 4

Determine if the equation is a differential equation.

*x*^{2} + *y*^{2} = 4*xy*

### Example 5

Determine if the equation is a differential equation.

### Example 6

Determine if the equation is a differential equation.

*y* + *y*^{2} + *y*^{3} = *x*

### Example 7

Determine if the equation is a differential equation.

### Example 8

Determine if the equation is a differential equation.

*y*' + 2*y*'' = 3 – *x*

### Example 9

Determine the order of the differential equation.

### Example 10

Determine the order of the differential equation.

*y*" + *y*' – *y* = 0

### Example 11

Determine the order of the differential equation.

*f* '(*x*) = *x*^{2} + 3*x* + 5

### Example 12

Determine the order of the differential equation.

*f* (*x*) – *f* ^{3}(*x*) + *f* ^{(2)} = 7*x*

### Example 13

Determine the order of the differential equation.