• Skip to main content
  • Skip to primary sidebar
  • Skip to footer
  • NCERT Solutions
    • NCERT Books Free Download
  • TS Grewal
    • TS Grewal Class 12 Accountancy Solutions
    • TS Grewal Class 11 Accountancy Solutions
  • CBSE Sample Papers
  • GSEB Solutions
  • Maharashtra Board
  • Kerala Board
    • Kerala Syllabus 9th Standard Physics Solutions Guide
    • Kerala Syllabus 9th Standard Biology Solutions Guide
  • Goa Board

CBSE Tuts

CBSE Maths notes, CBSE physics notes, CBSE chemistry notes

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.1

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.1 are part of NCERT Solutions for Class 12 Maths. Here we have given NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.1.

  • Differential Equations Class 12 Ex 9.2
  • Differential Equations Class 12 Ex 9.3
  • Differential Equations Class 12 Ex 9.4
  • 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 9.1
Number of Questions Solved 12
Category NCERT Solutions

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.1

Determine order and degree (if defined) of the differential equations given in Questions 1 to 10.

Ex 9.1 Class 12 Maths Question 1.
\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } +({ sin }y^{ III })=0
Solution:
Order of the equation is 4
It is not a polynomial in derivatives so that it
has not degree.

Ex 9.1 Class 12 Maths Question 2.
{ y }^{ I }+5y=0
Solution:
{ y }^{ I }+5y=0
It is a D.E. of order one and degree one.

Ex 9.1 Class 12 Maths Question 3.
{ \left( \frac { ds }{ dt } \right) }^{ 4 }+3s{ \left( \frac { { d }^{ 2 }s }{ { dt }^{ 2 } } \right) }=0
Solution:
Order of the equation is 2.
Degree of the equation is

Ex 9.1 Class 12 Maths Question 4.
{ \left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 2 }+cos\left( \frac { dy }{ dx } \right) =0
Solution:
{ \left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 2 }+cos\left( \frac { dy }{ dx } \right) =0
It is a D.E. of order 2 and degree undefined

Ex 9.1 Class 12 Maths Question 5.
\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =cos3x+sin3x
Solution:
\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =cos3x+sin3x
It is a D.E. of order 2 and degree 1.

Ex 9.1 Class 12 Maths Question 6.
{ { (y }^{ III }) }^{ 2 }+{ { ( }y^{ II }) }^{ 3 }+{ { (y }^{ I }) }^{ 4 }+{ y }^{ 5 }=0
Solution:
Order of the equation is 3
Degree of the equation is 2

Ex 9.1 Class 12 Maths Question 7.
{ { y }^{ III } }+{ 2y^{ II } }+{ { y }^{ I } }=0
Solution:
{ { y }^{ III } }+{ 2y^{ II } }+{ { y }^{ I } }=0
The highest order derivative is y.
Thus the order of the D.E. is 3.
The degree of D.E is 1

Ex 9.1 Class 12 Maths Question 8.
{ y }^{ I }+y={ e }^{ x }
Solution:
{ y }^{ I }+y={ e }^{ x }
The order of the D. E. = 1 (highest order derivative)
The degree of the D.E. = 1.

Ex 9.1 Class 12 Maths Question 9.
{ y }^{ III }+{ { (y }^{ I }) }^{ 2 }+2y=0
Solution:
{ y }^{ III }+{ { (y }^{ I }) }^{ 2 }+2y=0
The highest derivative is 2.
Order of the D.E. = 2.
Degree of the D. E = 1

Ex 9.1 Class 12 Maths Question 10.
{ y }^{ II }+{ { 2y }^{ I } }+siny=0
Solution:
Order of the equation is 2
Degree of the equation is 1

Ex 9.1 Class 12 Maths Question 11.
The degree of the differential equation
{ \left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 3 }{ +\left( \frac { dy }{ dx } \right) }^{ 2 }+sin{ \left( \frac { dy }{ dx } \right) }+1=0
(a) 3
(b) 2
(c) 1
(d) not defined
Solution:
{ \left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 3 }{ +\left( \frac { dy }{ dx } \right) }^{ 2 }+sin{ \left( \frac { dy }{ dx } \right) }+1=0
The degree not defined.
Because the differential equation can not be written as a polynomial in all the differential coefficients.
Hence option (d) is correct.

Ex 9.1 Class 12 Maths Question 12.
The order of the differential equation
{ 2x }^{ 2 }\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -3\frac { dy }{ dx } +y=0
(a) 2
(b) 1
(c) 0
(d) not defined
Solution:
{ 2x }^{ 2 }\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -3\frac { dy }{ dx } +y=0
Thus order of the D.E. = 2
Hence option (a) is correct.

We hope the NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.1 help you. If you have any query regarding NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.1, drop a comment below and we will get back to you at the earliest.

Primary Sidebar

NCERT Exemplar problems With Solutions CBSE Previous Year Questions with Solutoins CBSE Sample Papers

Recent Posts

  • MCQ Questions for Class 8 Science Chapter 18 Pollution of Air and Water with Answers
  • MCQ Questions for Class 8 Science Chapter 17 Stars and the Solar System with Answers
  • MCQ Questions for Class 8 Science Chapter 16 Light with Answers
  • MCQ Questions for Class 8 Science Chapter 15 Some Natural Phenomena with Answers
  • MCQ Questions for Class 8 Science Chapter 14 Chemical Effects of Electric Current with Answers
  • MCQ Questions for Class 8 Science Chapter 13 Sound with Answers
  • MCQ Questions for Class 8 Science Chapter 12 Friction with Answers
  • MCQ Questions for Class 8 Science Chapter 11 Force and Pressure with Answers
  • MCQ Questions for Class 8 Science Chapter 10 Reaching the Age of Adolescence with Answers
  • MCQ Questions for Class 8 Science Chapter 9 Reproduction in Animals with Answers
  • MCQ Questions for Class 8 Science Chapter 8 Cell Structure and Functions with Answers
  • MCQ Questions for Class 8 Science Chapter 7 Conservation of Plants and Animals with Answers
  • MCQ Questions for Class 8 Science Chapter 6 Combustion and Flame with Answers
  • MCQ Questions for Class 8 Science Chapter 5 Coal and Petroleum with Answers
  • MCQ Questions for Class 8 Science Chapter 4 Materials: Metals and Non-Metals with Answers

Footer

Maths NCERT Solutions

NCERT Solutions for Class 12 Maths
NCERT Solutions for Class 11 Maths
NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 9 Maths
NCERT Solutions for Class 8 Maths
NCERT Solutions for Class 7 Maths
NCERT Solutions for Class 6 Maths

SCIENCE NCERT SOLUTIONS

NCERT Solutions for Class 12 Physics
NCERT Solutions for Class 12 Chemistry
NCERT Solutions for Class 11 Physics
NCERT Solutions for Class 11 Chemistry
NCERT Solutions for Class 10 Science
NCERT Solutions for Class 9 Science
NCERT Solutions for Class 7 Science
MCQ Questions NCERT Solutions
CBSE Sample Papers
NCERT Exemplar Solutions LCM and GCF Calculator
TS Grewal Accountancy Class 12 Solutions
TS Grewal Accountancy Class 11 Solutions