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

### 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.

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