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

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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**.

Class 12th is a very crucial stage of your student’s
life, since you take all important decisions about your career on this stage.
Mathematics plays a vital role to take decision for your career because if you
are good in mathematics, you can choose engineering and technology field as
your career.

**NCERT
Solutions for Maths Class 12 Exercise 9.1** helps you to solve
each and every problem with step by step explanation which makes you strong in
mathematics.

All the schools affiliated with CBSE, follow the
NCERT books for all subjects. You can check your syllabus from **NCERT Syllabus for Mathematics Class 12**.

**NCERT
Solutions for Maths Class 12 Exercise 9.1** are prepared by the
experienced teachers of CBSE board. If you are preparing for JEE Mains and NEET
level exams, then it will definitely make your foundation strong.

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

If you want to recall **All** **Maths Formulas
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**

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**NCERT
Solutions for Maths Class 12 Exercise 9.6**

**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).

**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**

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**NCERT Solutions for Maths Class 12 Exercise 9.6**