NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.4 are part of NCERT Solutions for Class 12 Maths. Here we have given NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.4.
- Differential Equations Class 12 Ex 9.1
- Differential Equations Class 12 Ex 9.2
- Differential Equations Class 12 Ex 9.3
- Differential Equations Class 12 Ex 9.5
- Differential Equations Class 12 Ex 9.6
Board | CBSE |
Textbook | NCERT |
Class | Class 12 |
Subject | Maths |
Chapter | Chapter 9 |
Chapter Name | Differential Equations |
Exercise | Ex 9.4 |
Number of Questions Solved | 23 |
Category | NCERT Solutions |
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.
Solution:
integrating both sides, we get
Ex 9.4 Class 12 Maths Question 2.
Solution:
Ex 9.4 Class 12 Maths Question 3.
Solution:
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
Ex 9.4 Class 12 Maths Question 5.
Solution:
we have
Integrating on both sides
Ex 9.4 Class 12 Maths Question 6.
Solution:
integrating on both side we get
which is required solution
Ex 9.4 Class 12 Maths Question 7.
y logy dx – x dy = 0
Solution:
integrating we get
Ex 9.4 Class 12 Maths Question 8.
Solution:
Ex 9.4 Class 12 Maths Question 9.
solve the following
Solution:
integrating both sides we get
Ex 9.4 Class 12 Maths Question 10.
Solution:
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.
Solution:
here
integrating we get
Ex 9.4 Class 12 Maths Question 12.
Solution:
Ex 9.4 Class 12 Maths Question 13.
Solution:
Ex 9.4 Class 12 Maths Question 14.
Solution:
=> 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
Solution:
Ex 9.4 Class 12 Maths Question 16.
For the differential equation find the solution curve passing through the point (1,-1)
Solution:
The differential equation is
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
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 =
slope of the line joining (x, y) and (- 4, – 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 • then according to the question
Ex 9.4 Class 12 Maths Question 23.
The general solution of a differential equation is
(a)
(b)
(c)
(d)
Solution:
(a)
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