# Class 12 RD Sharma Solutions- Chapter 22 Differential Equations – Exercise 22.1 | Set 1

### Determine the order and degree of the following differential equation. State also whether it is linear or non-linear(Question 1-13)

### Question 1.

**Solution:**

We have,

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Order of function:The Highest order of derivative of function is 3 i.e.,

So, the order of derivative is equal to 3.

Degree of function:As the power of the highest order derivative of function is 1 (i.e., power of is 1)

So, degree of function is 1.

Linear or Non-linear:The given equation is non-linear.

### Question 2.

**Solution:**

We have,

Order of function:As the highest order of derivative of function is 2.(i.e.,)

So, Order of the function is equal to 2.

Degree of function:As the power of the highest order derivative of the function is 1(i.e., power of is 1)

So, Degree of the function is equal to 1.

Linear or Non-linear:The given equation is linear.

### Question 3.

**Solution**:

We have,

Order of function:As the highest order of derivative of function is 1 (i.e., )

So, Order of the function is equal to 1.

Degree of functionAs the power of the highest order derivative of the function is 3 (i.e., power of dy/dx is 3)

So, the degree of the function is equal to 3.

Linear or Non-linear:The given equation is non-linear.

### Question 4.

**Solution**:

We have,

On squaring both side, we get

On cubing both side, we get

Order of function:As the highest order of derivative of function is 2 (i.e.,

So, Oder of the function is equal to 2.

Degree of function:As the power of the highest order derivative of the function is 2. (i.e., power of is 2)

So, the Degree of the function is equal to 2.

Linear or Non-linear:The given equation is non-linear.

### Question 5.

**Solution:**

We have,

Order of function:As the highest order of derivative of function is 2

So, Order of the function is equal to 2.

Degree of function:As the power of the highest order derivative of function is 1 (i.e., power of is 1)

So, the Degree of the function is equal to 1.

Linear or Non-linear:The given equation is non-linear.

### Question 6.

**Solution**:

We have,

On cubing both side, we get

On squaring both side, we get

Order of function:As the highest order of derivative of function is 2 (i.e., )

So, the Order of the function is equal to 2.

Degree of function:As the power of the highest order derivative of the function is 2(i.e., power of is 2)

So, the Degree of the function is equal to 2.

Linear or Non-linear:The given equation is non-linear.

### Question 7.

**Solution**:

We have,

On squaring both side, we get

Oder of function:The highest order of derivative of function is 4 (i.e., )

So, the order of the derivative is equal to 4.

Degree of function:As the power of the highest order derivative of the function is 2 (i.e., power of is 2)

So, the degree of function is 2.

Linear or Non-linear:The given equation is non-linear.

### Question 8:

**Solution:**

We have,

On squaring both side, we have

Order of function:As the highest order of derivative of function is 1.

So, the Order of the function is equal to 1.

Degree of function:As the power of the highest order derivative of the function is 1.

So, the degree of the function is equal to 1.

Linear or Non-linear:The given equation is linear.

### Question 9:

**Solution:**

We have,

Order of function:As the highest order of derivative of function is 2 (i.e.,)

So, order of derivative is equal to 2.

Degree of function:As the power of the highest order derivative of the function is 1 (i.e., power of is 1)

So, the Degree of the function is equal to 1.

Linear or Non-linear:The given equation is linear.

### Question 10:

**Solution**:

We have,

Order of function:As the highest order of derivative of the function is 2.

So, the Order of the function is equal to 2.

Degree of function:As the power of the highest order derivative of the function is 1 (i.e., power of is 1)

So, the Degree of the function is equal to 1.

Linear or Non-linear:The given equation is non-linear.

### Question 11:

**Solution:**

We have,

Order of function:As the highest order of derivative of the function is 2

So, the Order of the function is equal to 2.

Degree of function:As the power of the highest order derivative of the function is 3. (i.e., power of is 3)

So, the degree of the function is equal to 3.

Linear or Non-linear:The given equation is non-linear.

### Question 12:

**Solution:**

We have,

Order of function:As the highest order of derivative of the function is 3

So, the Order of the function is equal to 3.

Degree of function:As the power of the highest order derivative of the function is 1.(i.e., power of is 1)

So, the Degree of the function is equal to 1.

Linear or Non-linear:The given equation is non-linear.

### Question 13:

**Solution**:

We have,

Order of function:As the highest order of derivative of the function is 1

So, the Order of the function is equal to 1.

Degree of function:As the power of the highest order derivative of the function is 1. (i.e., power of dy/dx is 1)

So, the Order of the function is equal to 1.

Linear or Non-linear:The given equation is non-linear.