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

Hello Students. Welcome to **maths-formula.com**. In this post, you will find the complete** ****NCERT Solutions for Maths Class 12 Exercise 9.6**.

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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 9.6** 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 9.6** 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.

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

**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**

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

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

**Find the general
solution of the following differential equations in Q.1 to 12.**

**Maths Class
12 Ex 9.6 Question 1.**

**Solution:**

Here, P = 2 and Q = sin x

Now, the
integrating factor (I.F.) is

Thus, the
solution of the given differential equation is

This is the
required general solution of the given differential equation.

**Maths Class
12 Ex 9.6 Question 2.**

**Solution:**

The given equation is a linear differential equation of the form;

Here, P = 3 and Q = *e ^{-2x}*

Now, the
integrating factor (I.F.) is

Thus, the
solution of the given differential equation is

This is the
required general solution of the given differential equation.

**Maths Class 12
Ex 9.6 Question 3.**

**Solution:**

The given equation is a linear differential equation of the form;

Here, P = 1/*x* and Q = *x*^{2}

Now, the integrating factor (I.F.) is

Thus, the
solution of the given differential equation is

This is the
required general solution of the given differential equation.

**Maths Class
12 Ex 9.6 Question 4.**

**Solution:**

The given equation is a linear differential equation of the form;

Here, P = sec *x* and Q = tan *x*

Now, the
integrating factor (I.F.) is

Thus, the
solution of the given differential equation is

This is the
required general solution of the given differential equation.

**Maths Class
12 Ex 9.6 Question 5.**

**Solution:**

The given differential equation can be written as

*dy*/

*dx*+ (sec

^{2}

*x*)

*y*= tan

*x*sec

^{2}

*x*

This differential equation is of the form;

Here, P = sec^{2} *x* and Q = tan
*x* sec^{2} *x*

Now, the
integrating factor (I.F.) is

Thus, the
solution of the given differential equation is

This is the
required general solution of the given differential equation.

**Maths Class
12 Ex 9.6 Question 6.**

**Solution:**

The given
differential equation can be written as *dy*/*dx* + 2*y*/*x *= *x* log *x*

This differential equation is of the form;

Here, P = 2/*x* and Q = *x* log *x*

Now, the
integrating factor (I.F.) is

Thus, the
solution of the given differential equation is

This is the
required general solution of the given differential equation.

**Maths Class
12 Ex 9.6 Question 7.**

**Solution:**

The given
differential equation is

This differential equation is of the form;

Here, P = 2/(*x* log *x*) and Q = 2/*x*^{2}

Now, the
integrating factor (I.F.) is

Thus, the
solution of the given differential equation is

This is the
required general solution of the given differential equation.

**Maths Class
12 Ex 9.6 Question 8.**

(1 + *x*²) *dy* + 2*xy dx* = cot *x dx* (*x* ≠ 0)

**Solution:**

The given
differential equation is (1 + *x*²) *dy* +
2*xy dx* = cot *x dx* (*x* ≠ 0)

Here, P = 2*x*/(1 + *x*^{2}) and Q = (cot *x*)/(1 + *x*^{2})

Thus, the
solution of the given differential equation is

This is the
required general solution of the given differential equation.

**Maths Class
12 Ex 9.6 Question 9.**

*x dy*/*dx* + *y*
– *x* + *xy* cot *x* = 0 (*x* ≠ 0)

**Solution:**

The given
differential equation is

Here, P = 1/*x* + cot *x* and Q = 1

Now, the
integrating factor (I.F.) is

Thus, the
solution of the given differential equation is

This is the
required general solution of the given differential equation.

**Maths Class
12 Ex 9.6 Question 10.**

(*x* + *y*) *dy*/*dx* = 1

**Solution:**

The given
differential equation is (*x* + *y*) *dy*/*dx*
= 1

Or *dx*/*dy*
*–* *x*
= *y *

This differential
equation is of the form *dx*/*dy* + *Px*
= *Q*;

Here, P = *–*1 and Q = *y*

Now, the
integrating factor (I.F.) is

Thus, the
solution of the given differential equation is

**Maths Class
12 Ex 9.6 Question 11.**

*y dx* + (*x* – *y*^{2})
*dy* = 0

**Solution:**

The given
differential equation is *y dx* + (*x* – *y*^{2}) *dy* = 0

Or *dx*/*dy*
+ *x*/*y* = *y *

This differential
equation is of the form *dx*/*dy* + *Px*
= *Q*;

Here, P = 1/*y* and Q = *y*

Now, the
integrating factor (I.F.) is

Thus, the
solution of the given differential equation is

**Maths Class
12 Ex 9.6 Question 12.**

(*x* + 3*y*^{2}) *dy*/*dx*
= *y* (*y* > 0)

**Solution:**

The given
differential equation is

*dx*/

*dy*+

*Px*=

*Q*;

Here, P = *–*1/*y* and Q = 3*y *

Now, the
integrating factor (I.F.) is

Thus, the
solution of the given differential equation is

This is the
required general solution of the given differential equation.

**For each of the
following Questions 13 to 15, find a particular solution satisfying the given
condition:**

**Maths Class
12 Ex 9.6 Question 13.**

**Solution:**

The given
differential equation is

This differential equation is of the form;

Here, P = 2 tan *x *and Q = sin *x*

Thus, the
solution of the given differential equation is

This is the
required particular solution of the given differential equation.

**Maths Class
12 Ex 9.6 Question 14.**

**Solution:**

The given
differential equation is

Thus, the
solution of the given differential equation is

This is the
required particular solution of the given differential equation.

**Maths Class
12 Ex 9.6 Question 15.**

**Solution:**

The given
differential equation is

This differential equation is of the form;

Here, P = –3 cot *x *and Q = sin 2*x *

Thus, the
solution of the given differential equation is

This is the
required particular solution of the given differential equation.

**Maths Class
12 Ex 9.6 Question 16.**

Find the equation
of the curve passing through the origin given that the slope of the tangent to
the curve at any point (*x*, *y*) is equal to the sum of the
coordinates of the point.

**Solution:**

The slope of the
a tangent to a curve is given by *dy*/*dx*.

This differential equation is of the form;

Here, P = –1 and Q = *x*

Now, the
integrating factor (I.F.) is

Thus, the
solution of the given differential equation is

This is the
required general solution of the given curve.

**Maths Class
12 Ex 9.6 Question 17.**

Find the equation of the curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.

**Solution:**

The slope of the
a tangent to a curve is given by *dy*/*dx*.

Now, from the
given condition, we get

This differential equation is of the form;

Here, P = –1 and Q = *x *– 5

Now, the
integrating factor (I.F.) is

Thus, the
solution of the given differential equation is

**Maths Class
12 Ex 9.6 Question 18.**

The integrating factor of the differential equationis

(A) *e*^{-x}

(B) *e*^{-y}

(C) 1/*x*

(D) *x*

**Solution:**

The given differential equation is

This differential equation is of the form;

Here, P = –1/*x *and Q = 2*x *

Thus, the integrating factor is

**Maths Class
12 Ex 9.6 Question 19.**

The integrating
factor of the differential equation(-1 < *y* < 1)
is

**Solution:**

The given
differential equation can be written as

Thus, the
integrating factor is

Hence, the
correct answer is option (D).

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

**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**

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