# NCERT Solutions For Class 12 Maths Chapter 9 Differential Equations Ex 9.4

Here, Below you all know about NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.4 Question Answer. I know many of you confuse about finding Chapter 9 Differential Equations Ex 9.4 Of Class 12 NCERT Solutions. So, Read the full post below and get your solutions.

Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 12 |

Subject | Maths |

Chapter | Chapter 9 |

Exercise | Class 12 Maths Chapter 9 Differential Equations Exercise 9.4 |

Number of Questions Solved | 23 |

## NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.4

**NCERT TEXTBOOK EXERCISES**

**Ex 9.4 Class 12 Maths Question 1.**

$\frac { dy }{ dx } =\frac { 1-cosx }{ 1+cosx }$

**Solution:**

$\frac { dy }{ dx } =\frac { 1-cosx }{ 1+cosx }$

$\frac { dy }{ dx } =\frac { 1-cosx }{ 1+cosx } =\frac { { 2sin }^{ 2 }\left( \frac { x }{ 2 } \right) }{ { 2cos }^{ 2 }\left( \frac { x }{ 2 } \right) } ={ tan }^{ 2 }\left( \frac { x }{ 2 } \right)$

integrating both sides, we get

**Ex 9.4 Class 12 Maths Question 2.**

$\frac { dy }{ dx } =\sqrt { 4-{ y }^{ 2 } } (-2<y<2)$

**Solution:**

$\frac { dy }{ dx } =\sqrt { 4-{ y }^{ 2 } } \Rightarrow \int { \frac { dy }{ \sqrt { { 4-y }^{ 2 } } } } =\int { dx }$

â‡’ $\Rightarrow { sin }^{ -1 }\frac { y }{ 2 } =x+C$

â‡’ $\Rightarrow y=2sin(x+C)$

**Ex 9.4 Class 12 Maths Question 3.**

$\frac { dy }{ dx } +y=1(y\neq 1)$

**Solution:**

$\frac { dy }{ dx } +y=1\Rightarrow \int { \frac { dy }{ y-1 } } =-\int { dx }$

$\Rightarrow log(y-1)=-x+c\Rightarrow y=1+{ e }^{ -x }.{ e }^{ c }$

Hencey=1+Ae^{âˆ’x}

which is required solution

**Ex 9.4 Class 12 Maths Question 4.**

secÂ² x tany dx+secÂ² y tanx dy = 0

**Solution:**

we have

secÂ² x tany dx+secÂ² y tanx dy = 0

**Ex 9.4 Class 12 Maths Question 5.**

$\left( { e }^{ x }+{ e }^{ -x } \right) dy-\left( { e }^{ x }-{ e }^{ -x } \right) dx=0$

**Solution:**

we have

$\left( { e }^{ x }+{ e }^{ -x } \right) dy-\left( { e }^{ x }-{ e }^{ -x } \right) dx=0$

Integrating on both sides

**Ex 9.4 Class 12 Maths Question 6.**

$\frac { dy }{ dx } =\left( { 1+x }^{ 2 } \right) \left( { 1+y }^{ 2 } \right)$

**Solution:**

$\frac { dy }{ { 1+y }^{ 2 } } =\left( { 1+x }^{ 2 } \right) dx$

integrating on both side we get

${ tan }^{ -1 }y={ x+\frac { 1 }{ 3 } }x^{ 3 }+c$

which is required solution

**Ex 9.4 Class 12 Maths Question 7.**

y logy dx â€“ x dy = 0

**Solution**

Undefined control sequence \because

integrating we get

**Ex 9.4 Class 12 Maths Question 8.**

${ x }^{ 5 }\frac { dy }{ dx } =-{ y }^{ 5 }$

**Solution:**

${ x }^{ 5 }\frac { dy }{ dx } =-{ y }^{ 5 }\Rightarrow \int { { y }^{ -5 }dy } =-\int { { x }^{ -5 }dx }$

$\Rightarrow -\frac { 1 }{ { y }^{ 4 } } =\frac { 1 }{ { x }^{ 4 } } +4c\Rightarrow { x }^{ -4 }+{ y }^{ -4 }=k$

**Ex 9.4 Class 12 Maths Question 9.**

solve the following

$\frac { dy }{ dx } ={ sin }^{ -1 }x$

**Solution:**

$\frac { dy }{ dx } ={ sin }^{ -1 }x\Rightarrow \int { dy } =\int { { sin }^{ -1 }xdx }$

integrating both sides we get

**Ex 9.4 Class 12 Maths Question 10.**

${ e }^{ x }tany\quad dx+{ (1-e }^{ x }){ sec }^{ 2 }dy=0$

**Solution:**

${ e }^{ x }tany\quad dx+{ (1-e }^{ x }){ sec }^{ 2 }dy=0$

we can write in another form

**Find a particular solution satisfying the given condition for the following differential equation in Q.11 to 14.**

**Ex 9.4 Class 12 Maths Question 11.**

$\left( { x }^{ 3 }+{ x }^{ 2 }+x+1 \right) \frac { dy }{ dx } ={ 2x }^{ 2 }+x;y=1,when\quad x=0$

**Solution:**

here

$dy=\frac { { 2x }^{ 2 }+x }{ \left( { x }^{ 3 }+{ x }^{ 2 }+x+1 \right) } dx$

integrating we get

**Ex 9.4 Class 12 Maths Question 12.**

$x\left( { x }^{ 2 }-1 \right) \frac { dy }{ dx } =1,y=0\quad when\quad x=2$

**Solution:**

$x\left( { x }^{ 2 }-1 \right) \frac { dy }{ dx } =1,y=0\quad when\quad x=2$

â‡’ $\Rightarrow \int { dy } =\int { \frac { dy }{ x(x+1)(x-1) } }$

**Ex 9.4 Class 12 Maths Question 13.**

$cos\left( \frac { dy }{ dx } \right) =a,(a\epsilon R),y=1\quad when\quad x=0$

**Solution:**

**Ex 9.4 Class 12 Maths Question 14.**

$\frac { dy }{ dx } =ytanx,y=1\quad when\quad x=0$

**Solution:**

$\frac { dy }{ dx } =ytanx\Rightarrow \int { \frac { dy }{ y } } =\int { tanx\quad dx }$

=> logy = logsecx + C

When x = 0, y = 1

=> log1 = log sec0 + C => 0 = log1 + C

=> C = 0

âˆ´ logy = log sec x

=> y = sec x.

**Ex 9.4 Class 12 Maths Question 15.**

Find the equation of the curve passing through the point (0,0) and whose differential equation ${ y }^{ I }={ e }^{ x }sinx$

**Solution:**

${ y }^{ I }={ e }^{ x }sinx$

$\Rightarrow dy={ e }^{ x }sinx\quad dx$

**Ex 9.4 Class 12 Maths Question 16.**

For the differential equation $xy\frac { dy }{ dx } =(x+2)(y+2)$ find the solution curve passing through the point (1,-1)

**Solution:**

The differential equation is $xy\frac { dy }{ dx } =(x+2)(y+2)$

or xydy=(x + 2)(y+2)dx

**Ex 9.4 Class 12 Maths Question 17.**

Find the equation of a curve passing through the point (0, -2) given that at any point (pc, y) on the curve the product of the slope of its tangent and y-coordinate of the point is equal to the x-coordinate of the point

**Solution:**

According to the question $y\frac { dy }{ dx } =x$

$\Rightarrow \int { ydy } =\int { xdx } \Rightarrow \frac { { y }^{ 2 } }{ 2 } =\frac { { x }^{ 2 } }{ 2 } +c$

0, â€“ 2) lies on it.c = 2

âˆ´ Equation of the curve is : xÂ² â€“ yÂ² + 4 = 0.

**Ex 9.4 Class 12 Maths Question 18.**

At any point (x, y) of a curve the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (-4,-3) find the equation of the curve given that it passes through (- 2,1).

**Solution:**

Slope of the tangent to the curve = dy/dx

slope of the line joining (x, y) and (- 4, â€“ 3)

**Ex 9.4 Class 12 Maths Question 19.**

The volume of a spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and offer 3 seconds it is 6 units. Find the radius of balloon after t seconds.

**Solution:**

Let v be volume of the balloon.

**Ex 9.4 Class 12 Maths Question 20.**

In a bank principal increases at the rate of r% per year. Find the value of r if Rs 100 double itself in 10 years

**Solution:**

Let P be the principal at any time t.

According to the problem

**Ex 9.4 Class 12 Maths Question 21.**

In a bank principal increases at the rate of 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years

**Solution:**

Let p be the principal Rate of interest is 5%

**Ex 9.4 Class 12 Maths Question 22.**

In a culture the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000 if the rate of growth of bacteria is proportional to the number present

**Solution:**

Let y denote the number of bacteria at any instant t â€¢ then according to the question

**Ex 9.4 Class 12 Maths Question 23.**

The general solution of a differential equation $\frac { dy }{ dx } ={ e }^{ x+y }$ is

(a) e^{x}+e^{âˆ’y}=c

(b) e^{x}+e^{y}=c

(c) e^{âˆ’x}+e^{y}=c

(d) e^{âˆ’x}+e^{âˆ’y}=c

**Solution:**

(a) $\frac { dy }{ dx } ={ e }^{ x }.{ e }^{ y }\Rightarrow \int { { e }^{ -y }dy } =\int { { e }^{ x }dx }$

$\Rightarrow { e }^{ -y }={ e }^{ x }+k\Rightarrow { e }^{ x }+{ e }^{ -y }=c$

## NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.4 PDF

For NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.4, you may click on the link below and get your NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise pdf file.

Finally, You all know about NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.4. If you have any questions, then comment below and share this post with others.

### Other Chapter of Class 12 Maths Chapter 9 Differential Equations

**Class 12 Maths Chapter 9 Differential Equations Ex 9.1****Class 12 Maths Chapter 9 Differential Equations Ex 9.2****Class 12 Maths Chapter 9 Differential Equations Ex 9.3****Class 12 Maths Chapter 9 Differential Equations Ex 9.4****Class 12 Maths Chapter 9 Differential Equations Ex 9.5****Class 12 Maths Chapter 9 Differential Equations Ex 9.6**