Here we provide RD Sharma Class 12 Ex 22.1 Solutions Chapter 22 Differential Equations for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Class 12 Ex 22.1 Solutions Chapter 22 Differential Equations book pdf download. Now you will get step-by-step solutions to each question.

Textbook | NCERT |

Class | Class 12th |

Subject | Maths |

Chapter | 22 |

Exercise | 22.1 |

Category | RD Sharma Solutions |

**RD Sharma Class 12 Ex 22.1 Solutions Chapter 22 Differential Equations**

### 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,

**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 function**

As 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, 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 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

**Order 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.

### Determine the order and degree of the following differential equation. State also whether it is linear or non-linear(Question 14-26)

### Question 14.

**Solution**:

We have,

**Order of function:**

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

So, the order of the derivative 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 degree of function is 1.

**Linear or Non-linear:**

The given equation is non-linear.

### Question 15.

**Solution:**

We have,

On cubing both side, we have

**Order of function:**

The Highest order of derivative of function is 2. (i.e., )

So, the order of the derivative 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 function is 3.

**Linear or Non-linear:**

The given equation is non-linear.

### Question 16.

**Solution:**

We have,

Squaring both sides, we have

**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 17.

**Solution:**

We have,

One squaring both side, we have

**Order of function:**

As the highest order of derivative of the 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 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 18.

**Solution:**

We have,

On squaring both sides, we get

**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 2.(i.e., power of dy/dx is 2)

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

**Linear or Non-linear:**

The given equation is non-linear.

### Question 19. , where p = dy/dx

**Solution:**

We have

, where p = dy/dx

**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 2 (i.e., power of dy/dx is 2)

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

**Linear or Non-linear:**

The given equation is non-linear.

### Question 20: dy/dx + e^{y }= 0

**Solution**:

We have,

dy/dx + e

^{y }= 0

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 Degree of the function is equal to 1.

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

### Question 21.

**Solution**:

We have,

**Order of function:**

As the highest order of derivative of the function is 2

So, the order of the derivative is equal to 2.

**Degree of function:**

is not a polynomial function. So degree can not be defined.

So, the degree of function is not defined.

**Linear or Non-linear:**

The given equation is non-linear.

### Question 22. (y”)^{2 }+ (y’)^{3} + siny = 0

**Solution:**

We have,

(y”)^{2 }+ (y’)^{3} + siny = 0

Where

**Order of function:**

The highest order of derivative of the function is 2. (i.e., y”)

So, the order of the derivative is equal to 2.

**Degree of function**

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

So, the degree of function is 2.

**Linear or Non-linear:**

The given equation is non-linear.

### Question 23.

**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 24.

**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 linear.

### Question 25.

**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.

**The degree of function:**

is not a polynomial function. So degree can not be defined.

So, the degree of function is not defined.

**Linear or Non-linear:**

The given equation is non-linear.

### Question 26.

**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 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.

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