Hello Students. In this post, you
will find the complete** ****NCERT Solutions for Maths Class
12 Exercise 9.1**.

You can download the **PDF of NCERT Books Maths Chapter 9** for your easy reference while studying **NCERT Solutions for Maths Class
12 Exercise 9.1**.

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NCERT books for all subjects. You can check your syllabus from **NCERT Syllabus for Mathematics Class 12**.

If you want to recall **All Maths Formulas for Class 12**, you can find it by clicking this link.

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for Class 11**, you can find it by clicking this link.

**NCERT Solutions for Maths Class 12 Exercise 9.2**

**NCERT Solutions for Maths Class 12 Exercise 9.3**

**NCERT Solutions for Maths Class 12 Exercise 9.4**

**NCERT Solutions for Maths Class 12 Exercise 9.5**

**NCERT Solutions for Maths Class 12 Exercise 9.1**

**Determine order
and degree (if defined) of the differential equations given in Exercises 1 to
10.**

**Maths Class
12 Ex 9.1 Question 1.**

**Solution:**

The given differential equation is

The highest order derivative
present in this differential equation is *d*^{4}*y*/*dx*^{4}
and its order is 4. So, the order of the differential equation is 4.

The given differential equation is
not a polynomial equation in derivatives as the term sin (*y*’’’) is a trigonometric function of derivative *y*’’’. Therefore, the degree is not
defined.

Hence, the order of the given
differential equation is 4 and its degree is not defined.

**Maths Class
12 Ex 9.1 Question 2.**

*y*’ + 5*y* = 0

**Solution:**

The given
differential equation is *y*’ + 5*y* = 0

The highest order derivative
present in this differential equation is *y*’ and its order
is 1. So, the order of the differential equation is 1.

The given differential equation is
a polynomial equation in derivatives and the highest power raised to the
highest order derivative *y*’ is 1.
Therefore, its degree is 1.

Hence, the order of the given differential equation is 1 and its
degree is 1.

**Maths Class
12 Ex 9.1 Question 3.**

**Solution:**

The given
differential equation is

The highest order derivative
present in this differential equation is *d*^{2}*s*/*dt*^{2}
and its order is 2. So, the order of the differential equation is 2.

The given differential equation is
a polynomial equation in derivatives and the highest power raised to the highest
order derivative *d*^{2}*s*/*dt*^{2} is 1. Therefore, its degree is 1.

Hence, the order of the given differential equation is 2 and its
degree is 1.

**Maths Class
12 Ex 9.1 Question 4.**

**Solution:**

The given differential equation is

The highest order derivative
present in this differential equation is *d*^{2}*y*/*dx*^{2}
and its order is 2. So, the order of the differential equation is 2.

The given differential equation is
not a polynomial equation in derivatives as the term cos (*dy*/*dx*) is a trigonometric
function of derivative *dy*/*dx*. Therefore, the degree is not
defined.

Hence, the order of the given differential equation is 2 and its
degree is not defined.

**Maths Class
12 Ex 9.1 Question 5.**

**Solution:**

The given
differential equation is

The highest order derivative
present in this differential equation is *d*^{2}*y*/*dx*^{2}
and its order is 2. So, the order of the differential equation is 2.

The given differential equation is
a polynomial equation in derivatives and the highest power raised to the
highest order derivative *d*^{2}*y*/*dx*^{2} is 1. Therefore, its degree is 1.

Hence, the order of the given differential equation is 2 and its
degree is 1.

**Maths Class
12 Ex 9.1 Question 6.**

(*y*’’’)^{2} + (*y*’’)^{3} + (*y*’)^{4} + *y*^{5}
= 0

**Solution:**

The given
differential equation is (*y*’’’)^{2} + (*y*’’)^{3} + (*y*’)^{4} + *y*^{5}
= 0

The highest order derivative
present in this differential equation is *y*’’’ and its order is 3. So, the order of the differential equation
is 3.

The given differential equation is
a polynomial equation in derivatives and the highest power raised to the
highest order derivative *y*’’’ is 2. Therefore, its degree
is 2.

Hence, the order of the given differential equation is 3 and its
degree is 2.

**Maths Class
12 Ex 9.1 Question 7.**

*y*’’’ + 2*y*’’ + *y*’ = 0

**Solution:**

The given
differential equation is *y*’’’ + 2*y*’’ + *y*’ = 0

The highest order
derivative present in this differential equation is *y*’’’ and its order is
3.
So, the order of the
differential equation is 3.

The given differential equation is
a polynomial equation in derivatives and the highest power raised to the
highest order derivative *y*’’’ is 1. Therefore, its degree
is 1.

Hence, the order of the given differential equation is 3 and its
degree is 1.

**Maths Class
12 Ex 9.1 Question 8.**

*y*’ + *y* = *e ^{x}*

**Solution:**

The given
differential equation is *y*’ + *y* = *e ^{x }*

The highest order
derivative present in this differential equation is *y*’ and its order is
1.
So, the order of the
differential equation is 1.

The given differential equation is
a polynomial equation in derivatives and the highest power raised to the
highest order derivative *y*’ is 1. Therefore, its degree
is 1.

Hence, the order of the given differential equation is 1 and its
degree is 1.

**Maths Class
12 Ex 9.1 Question 9.**

*y*’’ + (*y*’)^{2} + 2*y* = 0

**Solution:**

The given
differential equation is *y*’’ + (*y*’)^{2} + 2*y* = 0

The highest order
derivative present in this differential equation is *y*’’ and its order is
2.
So, the order of the
differential equation is 2.

The given differential equation is
a polynomial equation in derivatives and the highest power raised to the
highest order derivative *y’’* is
1. Therefore, its degree is 1.

Hence, the order of the given differential equation is 2 and its
degree is 1.

**Maths Class
12 Ex 9.1 Question 10.**

*y*’’ + 2*y*’ + sin *y* = 0

**Solution:**

The given
differential equation is *y*’’ + 2*y*’ + sin *y* = 0

The highest order
derivative present in this differential equation is *y*’’ and its order is
2.
So, the order of the
differential equation is 2.

The given differential equation is
a polynomial equation in derivatives and the highest power raised to the
highest order derivative *y’’* is
1. Therefore, its degree is 1.

Hence, the order of the given differential equation is 2 and its
degree is 1.

**Maths Class
12 Ex 9.1 Question 11.**

The degree of the differential equation is

(A) 3

(B) 2

(C) 1

(D) not defined

**Solution:**

The given differential equation is

*dy*/

*dx*) is a trigonometric function of derivative

*dy*/

*dx*. Therefore, the degree is not defined.

Hence, the
correct answer is option (D).

**Maths Class
12 Ex 9.1 Question 12.**

The order of the differential equation is

(A) 2

(B) 1

(C) 0

(D) not defined

**Solution:**

The given differential equation is

*d*

^{2}

*y*/

*dx*

^{2}and its order is 2. So, the order of the differential equation is 2.

Hence, the
correct answer is option (A).

**Related Links:**

**NCERT Solutions for Maths Class 12 Exercise 9.2**

**NCERT Solutions for Maths Class 12 Exercise 9.3**