### Determine order and degree (if defined) of differential equations given in exercises 1 to 10.

### Question 1.

**Solution:**

Given:

Here the order is 4 and degree is not defined because it is not a polynomial function.

### Question 2. y’ + 5y = 0

**Solution:**

Given: y’ + 5y = 0

Here, the order is 1 and the degree is also 1.

### Question 3.

**Solution:**

Given:

Here, the order is 2 and the degree is 1.

### Question 4.

**Solution:**

Given:

Here, the order is 2 and degree is not defined because it is not a polynomial function.

### Question 5.

**Solution:**

Given:

Here, the order is 2 and degree is 1.

### Question 6. (y”’)^{2 }+ (y”)^{3} + y(‘)^{4} + y^{5 }= 0

**Solution:**

Given: (y”’)

^{2 }+ (y”)^{3}+ y(‘)^{4}+ y^{5 }= 0The order is 3 and the degree is 2.

### Question 7. y” + 2y” + y’ = 0

**Solution:**

Given: y”’ + 2y” + y’ = 0

The order is 3 and the degree is 1

### Question 8. y’ + y = e^{x}

**Solution:**

Given: y’ + y = e

^{x}The order is 1 and the degree is 1.

### Question 9. y” + (y’)^{2} + 2y = 0

**Solution:**

Given: y” + (y’)

^{2 }+ 2y = 0The order is 3 the degree is 1

### Question 10. y” + 2y’ + sin y = 0

**Solution:**

Given: y” + 2y’ + sin y = 0

The order is 2 and the degree is one.

### Question 11. The degree of the differential equation

### is

### (A) 3 (B) 2 (C) 1 (D) Not defined

**Solution:**

Given:

Here, the degree is not defined.

So, the correct option is D.

### Question 12. The order of the differential equation

### is

### (A) 3 (B) 2 (C) 1 (D) Not defined

**Solution:**

Given:

Here, the order is 2.

So, the correct option is A.