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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.

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.

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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.

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