NCERT Solutions for Class 12 Maths Exercise 9.2 Chapter 9 Differential Equations – FREE PDF Download
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NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations (Ex 9.2) Exercise 9.2
In each of the Questions 1 to 6 verify that the given functions (explicit) is a solution of the corresponding differential equation:
1.
……….(i) To prove: y is a solution of the differential equation 
……….(ii)
Proof: From eq. (i), 
and
∴∴L.H.S. of eq. (ii),
= R.H.S.
Hence, y given by eq. (i) is a solution of .
2.
……….(i) To prove: y is a solution of the differential equation 
……….(ii)
Proof:From, eq. (i),
L.H.S. of eq. (ii),
= 
= 
= 
= R.H.S.
Hence, y given by eq. (i) is a solution of .
3.
……….(i) To prove: y is a solution of the differential equation 
……….(ii)
Proof: From eq. (i),
L.H.S. of eq. (ii),
= R.H.S.
Hence, y given by eq. (i) is a solution of .
4.
……….(i) To prove:y is a solution of the differential equation 
……….(ii)
Proof: From eq. (i),
= 
= 
= 
………(iii)
Now R.H.S. of eq. (ii)
= 
= 
[From eq. (i)]
= = 
L.H.S. = R.H.S
Hence, y given by eq. (i) is a solution of .
5.
……….(i) To prove:y given by eq. (i) is a solution of differential equation 
……….(ii)
Proof: From eq. (i)
L.H.S. of eq. (ii)
= 
= 
= 
= R.H.S. of eq. (ii)
y given by eq. (i) is a solution of differential equation .
6.
……….(i) To prove:y given by eq. (i) is a solution of differential equation 
..(ii)
Proof: From eq. (i),
= 
L.H.S. of eq. (ii)
= 
R.H.S. of eq. (ii)
= 
= 
[From eq. (i)]
= 
= 
= 
= 
= 
L.H.S. = R.H.S
Hence, y given by eq. (i) is a solution of .
In each of the questions 7 to 10, verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:
7.
……….(i) To prove:y given by eq. (i) is a solution of differential equation 
…….(ii)
Proof: Differentiating both sides of eq. (i) w.r.t x, we have
⟹y′=−y2xy−1⟹y′=−y2xy−1
Hence, Function (implicit) given by eq. (i) is a solution of .
8.
……….(i) To prove: y given by eq. (i) is a solution of differential equation
……….(ii)
Proof: Differentiating both sides of eq. (i) w.r.t x, we have
……….(iii)
Putting the value of x from eq. (i) and value of y’ from eq. (iii) in L.H.S. of eq. (ii),
= R.H.S. of (ii)
Hence, Function given by eq. (i) is a solution of .
9.
……….(i) To prove:y given by eq. (i) is a solution of differential equation 
….(ii)
Proof: Differentiating both sides of eq. (i) w.r.t x we have
= eq. (ii)
Hence, Function given by eq. (i) is a solution of
10.
……….(i) To prove:y given by eq. (i) is a solution of differential equation 
……(ii)
Proof: From eq. (i),
dydxdydx= 
= 
……….(iii)
Putting the values of y and 
from eq. (i) and (iii) in L.H.S. of eq. (ii),
= 
= 
= 
= R.H.S. of eq. (ii)
Hence, Function given by eq. (i) is a solution of .
Choose the correct answer:
11. The number of arbitrary constants in the general solution of a differential equation of fourth order are:
(A) 0
(B) 2
(C) 3
(D) 4
The number of arbitrary constants (
etc.) in the general solution of a differential equation of 
order is 
12. The number of arbitrary constants in the particular solution of a differential equation of third order are:
(A) 3
(B) 2
(C) 1
(D) 0
Therefore, option (D) is correct.