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

Get Free NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.4 PDF in Hindi and English Medium. Sets Class 12 Maths NCERT Solutions are extremely helpful while doing your homework. Differential Equations Exercise 9.4 Class 12 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 9 Class 12 Differential Equations Ex 9.4 provided in NCERT Textbook.

Free download NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.4 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

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

For each of the following D.E in Q. 1 to 10 find the general solution:

Ex 9.4 Class 12 Maths Question 1.
Image may be NSFW.
Clik here to view. $\frac { dy }{ dx } =\frac { 1-cosx }{ 1+cosx }$
Solution:
Image may be NSFW.
Clik here to view. $\frac { dy }{ dx } =\frac { 1-cosx }{ 1+cosx }$
Image may be NSFW.
Clik here to view. $\frac { dy }{ dx } =\frac { 1-cosx }{ 1+cosx } =\frac { { 2sin }^{ 2 }\left( \frac { x }{ 2 } \right) }{ { 2cos }^{ 2 }\left( \frac { x }{ 2 } \right) } ={ tan }^{ 2 }\left( \frac { x }{ 2 } \right)$
integrating both sides, we get
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 1

Ex 9.4 Class 12 Maths Question 2.
Image may be NSFW.
Clik here to view. $\frac { dy }{ dx } =\sqrt { 4-{ y }^{ 2 } } (-2<y<2)$
Solution:
Image may be NSFW.
Clik here to view. $\frac { dy }{ dx } =\sqrt { 4-{ y }^{ 2 } } \Rightarrow \int { \frac { dy }{ \sqrt { { 4-y }^{ 2 } } } } =\int { dx }$
Image may be NSFW.
Clik here to view. $\Rightarrow { sin }^{ -1 }\frac { y }{ 2 } =x+C$
Image may be NSFW.
Clik here to view. $\Rightarrow y=2sin(x+C)$

Ex 9.4 Class 12 Maths Question 3.
Image may be NSFW.
Clik here to view. $\frac { dy }{ dx } +y=1(y\neq 1)$
Solution:
Image may be NSFW.
Clik here to view. $\frac { dy }{ dx } +y=1\Rightarrow \int { \frac { dy }{ y-1 } } =-\int { dx }$
Image may be NSFW.
Clik here to view. $\Rightarrow log(y-1)=-x+c\Rightarrow y=1+{ e }^{ -x }.{ e }^{ c }$
Image may be NSFW.
Clik here to view. $Hence\quad y=1+{ Ae }^{ -x }$
which is required solution

Ex 9.4 Class 12 Maths Question 4.
sec² x tany dx+sec² y tanx dy = 0
Solution:
we have
sec² x tany dx+sec² y tanx dy = 0
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 4

Ex 9.4 Class 12 Maths Question 5.
Image may be NSFW.
Clik here to view. $\left( { e }^{ x }+{ e }^{ -x } \right) dy-\left( { e }^{ x }-{ e }^{ -x } \right) dx=0$
Solution:
we have
Image may be NSFW.
Clik here to view. $\left( { e }^{ x }+{ e }^{ -x } \right) dy-\left( { e }^{ x }-{ e }^{ -x } \right) dx=0$
Integrating on both sides
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 5

Ex 9.4 Class 12 Maths Question 6.
Image may be NSFW.
Clik here to view. $\frac { dy }{ dx } =\left( { 1+x }^{ 2 } \right) \left( { 1+y }^{ 2 } \right)$
Solution:
Image may be NSFW.
Clik here to view. $\frac { dy }{ { 1+y }^{ 2 } } =\left( { 1+x }^{ 2 } \right) dx$
integrating on both side we get
Image may be NSFW.
Clik here to view. ${ tan }^{ -1 }y={ x+\frac { 1 }{ 3 } }x^{ 3 }+c$
which is required solution

Ex 9.4 Class 12 Maths Question 7.
y logy dx – x dy = 0
Solution:
Image may be NSFW.
Clik here to view. $\because \quad y\quad logy\quad dx=x\quad dy\Rightarrow \frac { dy }{ y\quad logy } =\frac { dx }{ x }$
integrating we get
Image may be NSFW.
Clik here to view. tiwari academy class 12 maths Chapter 9 Differential Equations 7

Ex 9.4 Class 12 Maths Question 8.
Image may be NSFW.
Clik here to view. ${ x }^{ 5 }\frac { dy }{ dx } =-{ y }^{ 5 }$
Solution:
Image may be NSFW.
Clik here to view. ${ x }^{ 5 }\frac { dy }{ dx } =-{ y }^{ 5 }\Rightarrow \int { { y }^{ -5 }dy } =-\int { { x }^{ -5 }dx }$
Image may be NSFW.
Clik here to view. $\Rightarrow -\frac { 1 }{ { y }^{ 4 } } =\frac { 1 }{ { x }^{ 4 } } +4c\Rightarrow { x }^{ -4 }+{ y }^{ -4 }=k$

Ex 9.4 Class 12 Maths Question 9.
solve the following
Image may be NSFW.
Clik here to view. $\frac { dy }{ dx } ={ sin }^{ -1 }x$
Solution:
Image may be NSFW.
Clik here to view. $\frac { dy }{ dx } ={ sin }^{ -1 }x\Rightarrow \int { dy } =\int { { sin }^{ -1 }xdx }$
integrating both sides we get
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 9

Ex 9.4 Class 12 Maths Question 10.
Image may be NSFW.
Clik here to view. ${ e }^{ x }tany\quad dx+{ (1-e }^{ x }){ sec }^{ 2 }dy=0$
Solution:
Image may be NSFW.
Clik here to view. ${ e }^{ x }tany\quad dx+{ (1-e }^{ x }){ sec }^{ 2 }dy=0$
we can write in another form
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 10

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.
Image may be NSFW.
Clik here to view. $\left( { x }^{ 3 }+{ x }^{ 2 }+x+1 \right) \frac { dy }{ dx } ={ 2x }^{ 2 }+x;y=1,when\quad x=0$
Solution:
here
Image may be NSFW.
Clik here to view. $dy=\frac { { 2x }^{ 2 }+x }{ \left( { x }^{ 3 }+{ x }^{ 2 }+x+1 \right) } dx$
integrating we get
Image may be NSFW.
Clik here to view. tiwari academy class 12 maths Chapter 9 Differential Equations 11

Ex 9.4 Class 12 Maths Question 12.
Image may be NSFW.
Clik here to view. $x\left( { x }^{ 2 }-1 \right) \frac { dy }{ dx } =1,y=0\quad when\quad x=2$
Solution:
Image may be NSFW.
Clik here to view. $x\left( { x }^{ 2 }-1 \right) \frac { dy }{ dx } =1,y=0\quad when\quad x=2$
Image may be NSFW.
Clik here to view. $\Rightarrow \int { dy } =\int { \frac { dy }{ x(x+1)(x-1) } }$
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 12
Image may be NSFW.
Clik here to view.

Ex 9.4 Class 12 Maths Question 13.
Image may be NSFW.
Clik here to view. $cos\left( \frac { dy }{ dx } \right) =a,(a\epsilon R),y=1\quad when\quad x=0$
Solution:
Image may be NSFW.
Clik here to view. $cos\left( \frac { dy }{ dx } \right) =a\quad \therefore \frac { dy }{ dx } ={ cos }^{ -1 }a$
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 13

Ex 9.4 Class 12 Maths Question 14.
Image may be NSFW.
Clik here to view. $\frac { dy }{ dx } =ytanx,y=1\quad when\quad x=0$
Solution:
Image may be NSFW.
Clik here to view. $\frac { dy }{ dx } =ytanx\Rightarrow \int { \frac { dy }{ y } } =\int { tanx\quad dx }$
=> logy = logsecx + C
When x = 0, y = 1
=> log1 = log sec0 + C => 0 = log1 + C
=> C = 0
∴ 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 Image may be NSFW.
Clik here to view. ${ y }^{ I }={ e }^{ x }sinx$
Solution:
Image may be NSFW.
Clik here to view. ${ y }^{ I }={ e }^{ x }sinx$
Image may be NSFW.
Clik here to view. $\Rightarrow dy={ e }^{ x }sinx\quad dx$
Image may be NSFW.
Clik here to view. tiwari academy class 12 maths Chapter 9 Differential Equations 15

Ex 9.4 Class 12 Maths Question 16.
For the differential equation Image may be NSFW.
Clik here to view. $xy\frac { dy }{ dx } =(x+2)(y+2)$ find the solution curve passing through the point (1,-1)
Solution:
The differential equation isImage may be NSFW.
Clik here to view. $xy\frac { dy }{ dx } =(x+2)(y+2)$
or xydy=(x + 2)(y+2)dx
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 16

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 Image may be NSFW.
Clik here to view. $y\frac { dy }{ dx } =x$
Image may be NSFW.
Clik here to view. $\Rightarrow \int { ydy } =\int { xdx } \Rightarrow \frac { { y }^{ 2 } }{ 2 } =\frac { { x }^{ 2 } }{ 2 } +c$
0, – 2) lies on it.c = 2
∴ Equation of the curve is : x² – y² + 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 = Image may be NSFW.
Clik here to view. $\frac { dy }{ dx }$
slope of the line joining (x, y) and (- 4, – 3)
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 18
Image may be NSFW.
Clik here to view. tiwari academy class 12 maths Chapter 9 Differential Equations 18.1

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.
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 19

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
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 20

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%
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 21

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 • then according to the question
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 22

Ex 9.4 Class 12 Maths Question 23.
The general solution of a differential equation Image may be NSFW.
Clik here to view. $\frac { dy }{ dx } ={ e }^{ x+y }$ is
(a) Image may be NSFW.
Clik here to view. ${ e }^{ x }+{ e }^{ -y }=c$
(b) Image may be NSFW.
Clik here to view. ${ e }^{ x }+{ e }^{ y }=c$
(c) Image may be NSFW.
Clik here to view. ${ e }^{ -x }+{ e }^{ y }=c$
(d) Image may be NSFW.
Clik here to view. ${ e }^{ -x }+{ e }^{ -y }=c$
Solution:
(a) Image may be NSFW.
Clik here to view. $\frac { dy }{ dx } ={ e }^{ x }.{ e }^{ y }\Rightarrow \int { { e }^{ -y }dy } =\int { { e }^{ x }dx }$
Image may be NSFW.
Clik here to view. $\Rightarrow { e }^{ -y }={ e }^{ x }+k\Rightarrow { e }^{ x }+{ e }^{ -y }=c$

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

Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Exercise 9.4 of Differential Equations
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Exercise 9.4 for 2019-20
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view. ex. 9.4 class 12
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view. 12 Maths exercise 9.4 all questions
Image may be NSFW.
Clik here to view. ex 9.4 solutions
Image may be NSFW.
Clik here to view. 12 Maths Exercise 9.4 in Hindi medium
Image may be NSFW.
Clik here to view. Class 12 Maths Exercise 9.4 in PDF
Image may be NSFW.
Clik here to view. Solutions for Class 12 Maths Exercise 9.4 updated
Image may be NSFW.
Clik here to view. Ex 9.4 in Hindi medium