NCERT Solutions for Class 12 Maths Exercise 9.5 Chapter 9 Differential Equations – FREE PDF Download
Free PDF download of NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5 (Ex 9.5) and all chapter exercises at one place prepared by expert teacher as per NCERT (CBSE) books guidelines. Class 12 Maths Chapter 9 Differential Equations Exercise 9.5 Questions with Solutions to help you to revise complete Syllabus and Score More marks.
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations (Ex 9.5) Exercise 9.5
In each of the following Questions 1 to 5, show that the differential equation is homogenous and solve each of them:
1. 
……….(i) Here degree of each coefficients of 
and 
is same therefore, it is homogenous.
…..(ii)
F
,
therefore the given differential equation is homogeneous.
Putting 
Putting value of 
and 
in eq. (ii),
[Separating variables]
Integrating both sides,
=> 
Putting 
where C = 
2. 
……….(i)
Therefore, eq. (i) is homogeneous.
Putting
Putting value of 
and in eq. (i)
=> 
[Separating variables]
Integrating both sides,
=> 
Putting ,
=> 
3.
……….(i) This given equation is homogeneous because each coefficients of and is of degree 1.
Putting
….(ii)
Putting value of and in eq. (ii)
=>xdvdx=1+v−v+v21−v=>xdvdx=1+v−v+v21−v
=>xdvdx=1+v21−v=>xdvdx=1+v21−v
[Separating variables]
Integrating both sides,
=> 
Putting ,
=>
4.
– This equation is homogeneous because degree of each coefficient of and is same i.e., 2
……….(ii)
Therefore, the given equation is homogeneous.
Put
Putting these values of and in eq. (ii), we get
xdvdx=v2−1−2v22vxdvdx=v2−1−2v22v
Integrating both sides,
=> 
Put ,
=> 
5.
= 
……….(i)
Therefore, the given differential equation is homogeneous as all terms of 
and are of same degree i.e., degree 2.
Putting
Putting these values of and in eq. (i), we get
[Separating variables]
Integrating both sides,
=> 
= 
Putting ,
=> 
=
=> 
=
In each of the Questions 6 to 10, show that the given differential equation is homogeneous and solve each of them:
6. 
[Dividing by ]
Therefore given differential equation is homogeneous.
Putting
Putting these values of and in eq. (i), we get
=> 
Integrating both sides,
Putting ,
7.
……….(i)
Therefore, the given differential equation is homogeneous.
Putting
Putting these values of and in eq. (i), we get
[Separating variables]
Integrating both sides,
log∣∣secvv∣∣=log|c|x2log|secvv|=log|c|x2
Putting 
=> 
where C = 
8.
= ……….(i)
Therefore, the given differential equation is homogeneous.
Putting
Putting these values of and in eq. (i), we get
Integrating both sides,
=> 
[putting ]
where 
9.
……….(i)
Therefore, the given differential equation is homogeneous.
Putting
Putting these values of and in eq. (i), we get
= 
Integrating both sides,
where C =
[Putting ]
10.
[Dividing by ]
……….(i)
Therefore, it is a homogeneous.
Now putting 
Putting these values of 
and 
in eq. (i), we have
[Separating variables]
Integrating both sides,
Now putting 
,
C where C =
For each of the differential equations in Questions from 11 to 15, find the particular solution satisfying the given condition
11. 
when 
when …..(i) (x+y)dy+(x-y)dx=0
……….(ii)
Therefore the given differential equation is homogeneous because each coefficient of and 
is same i.e., degree 1.
Putting 
Putting these values of and 
in eq. (ii), we have
[Separating variables]
Integrating both sides,
=> 
Now putting
12log(y2+x2)−12×2logx+tan−1yx=−logx+c12log(y2+x2)−12×2logx+tan−1yx=−logx+c
……….(iii)
Now again given 
when , therefore putting these values in eq. (iii),
Putting this value of 
in eq. (iii), we get
log(y2+x2)+2tan−1yx=log2+π4log(y2+x2)+2tan−1yx=log2+π4
12. when
when
x2dy=−(xy+y2)dxx2dy=−(xy+y2)dx
……….(i)
Therefore the given differential equation is homogeneous.
Putting
Putting these values of and in eq. (i), we have
Integrating both sides,
Putting
where C = ……….(ii)
Now putting and in eq. (ii), we get 1 = 3C 
Putting value of C in eq. (ii),
13. when
when
= ……….(i)
Therefore, the given differential equation is homogeneous.
Putting
Putting these values of 
and in eq. (i), we have
[Separating variables]
Integrating both sides,
[Putting ] ……….(ii)
Now putting 
in eq. (ii),
Putting the value of in eq. (ii),
14. when
when 
………(i)
Therefore, the given differential equation is homogeneous.
Putting
Putting these values of and in eq. (i), we have
[Separating variables]
Integrating both sides,
[Putting ] ……….(ii)
Now putting 
in eq. (ii),
Putting the value of in eq. (ii),
15. when
when
……….(i) 
……….(ii)
Therefore the given differential equation is homogeneous because each coefficient of and is same.
Putting
Putting these values of and in eq. (ii), we have
[Separating variables]
Integrating both sides,
[Putting ]
Now putting 
in ,
Again putting , in 
, we get
Choose the correct answer:
16. A homogeneous differential equation of the form 
can be solved by making the substitution:
(A)
(B) 
(C) 
(D) 
can be solved by the substitution 
i.e., 
Therefore, option (C) is correct.
17. Which of the following is a homogeneous differential equation:
(A) 
(B) 
(C) 
(D) 