NCERT Solutions for Class 12 Maths Chapter 9 – Differential Equations Ex 9.1
Page No 382:
Question 1:
Determine order and degree(if defined) of differential equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7768/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_m16365a44.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7768/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_m16365a44.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7768/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_53630ae1.gif)
The highest order derivative present in the differential equation is
. Therefore, its order is four.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7768/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_m3eaf3523.gif)
The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined.
Question 2:
Determine order and degree(if defined) of differential equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7770/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_111495ce.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7770/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_111495ce.gif)
Answer:
The given differential equation is:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7770/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_111495ce.gif)
The highest order derivative present in the differential equation is
. Therefore, its order is one.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7770/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_7ae65614.gif)
It is a polynomial equation in
. The highest power raised to
is 1. Hence, its degree is one.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7770/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_7ae65614.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7770/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_7ae65614.gif)
Question 3:
Determine order and degree(if defined) of differential equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7772/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_5715334e.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7772/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_5715334e.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7772/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_mfd55bae.gif)
The highest order derivative present in the given differential equation is
. Therefore, its order is two.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7772/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_m2018a44e.gif)
It is a polynomial equation in
and
. The power raised to
is 1.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7772/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_m2018a44e.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7772/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_m2bf8115e.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7772/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_m2018a44e.gif)
Hence, its degree is one.
Question 4:
Determine order and degree(if defined) of differential equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7773/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_682788d.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7773/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_682788d.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7773/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_682788d.gif)
The highest order derivative present in the given differential equation is
. Therefore, its order is 2.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7773/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_48519442.gif)
The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined.
Question 5:
Determine order and degree(if defined) of differential equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7775/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_172ba5c.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7775/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_172ba5c.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7775/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_172ba5c.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7775/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_5d91d6c8.gif)
The highest order derivative present in the differential equation is
. Therefore, its order is two.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7775/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_48519442.gif)
It is a polynomial equation in
and the power raised to
is 1.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7775/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_48519442.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7775/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_48519442.gif)
Hence, its degree is one.
Question 6:
Determine order and degree(if defined) of differential equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7776/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_7a07ddee.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7776/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_7a07ddee.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7776/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_m76caf200.gif)
The highest order derivative present in the differential equation is
. Therefore, its order is three.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7776/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_ma6d2904.gif)
The given differential equation is a polynomial equation in
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7776/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_16ea1699.gif)
The highest power raised to
is 2. Hence, its degree is 2.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7776/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_ma6d2904.gif)
Question 7:
Determine order and degree(if defined) of differential equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7778/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_m218bf84.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7778/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_m218bf84.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7778/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_m218bf84.gif)
The highest order derivative present in the differential equation is
. Therefore, its order is three.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7778/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_ma6d2904.gif)
It is a polynomial equation in
. The highest power raised to
is 1. Hence, its degree is 1.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7778/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_cf6aa04.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7778/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_ma6d2904.gif)
Page No 383:
Question 8:
Determine order and degree(if defined) of differential equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7779/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_m23f19eec.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7779/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_m23f19eec.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7779/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_mbc99beb.gif)
The highest order derivative present in the differential equation is
. Therefore, its order is one.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7779/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_7ae65614.gif)
The given differential equation is a polynomial equation in
and the highest power raised to
is one. Hence, its degree is one.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7779/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_7ae65614.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7779/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_7ae65614.gif)
Question 9:
Determine order and degree(if defined) of differential equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7781/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_m6e313796.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7781/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_m6e313796.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7781/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_m6e313796.gif)
The highest order derivative present in the differential equation is
. Therefore, its order is two.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7781/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_9912cf3.gif)
The given differential equation is a polynomial equation in
and
and the highest power raised to
is one.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7781/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_9912cf3.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7781/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_7ae65614.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7781/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_9912cf3.gif)
Hence, its degree is one.
Question 10:
Determine order and degree(if defined) of differential equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7782/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_5e8fe0e5.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7782/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_5e8fe0e5.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7782/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_5e8fe0e5.gif)
The highest order derivative present in the differential equation is
. Therefore, its order is two.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7782/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_9912cf3.gif)
This is a polynomial equation in
and
and the highest power raised to
is one. Hence, its degree is one.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7782/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_9912cf3.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7782/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_7ae65614.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7782/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_9912cf3.gif)
Question 11:
The degree of the differential equation
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7783/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_62843805.gif)
(A) 3 (B) 2 (C) 1 (D) not defined
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7783/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_62843805.gif)
The given differential equation is not a polynomial equation in its derivatives. Therefore, its degree is not defined.
Hence, the correct answer is D.
Question 12:
The order of the differential equation
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7785/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_m28d16eac.gif)
(A) 2 (B) 1 (C) 0 (D) not defined
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7785/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_m28d16eac.gif)
The highest order derivative present in the given differential equation is
. Therefore, its order is two.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/238/7785/NCERT_12-11-08_Gopal_12_Maths_Ex-9.1_12_MNK_SG_html_48519442.gif)
Hence, the correct answer is A.