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

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

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

Question 1.
\(\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } +({ sin }y^{ “‘ })\) = 0
Solution:
The highest order derivatives is \(\frac { { d }^{ 4 }y }{ { dx }^{ 4 } }\)
∴ Order of the equation is 4
The differential equation is not a polynomial equation in its derivatives.
Hence its degree is not defined.

Question 2.
y’ + 5y = 0
Solution:
The highest order derivative is y’
∴ Order is 1
This is a polynomial equation in y’ and the
Hence its degree is 1.

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

Question 3.
\({ \left( \frac { ds }{ dt } \right) }^{ 4 }+3s{ \left( \frac { { d }^{ 2 }s }{ { dt }^{ 2 } } \right) }\) = 0
Solution:
The highest order derivative is \(\frac{d^{2} s}{d t^{2}}\)
∴ Order is 2
This is a polynomial equation in \(\frac{d^{2} s}{d t^{2}}\) and \(\frac{ds}{dt}\) and the power of \(\frac{d^{2} s}{d t^{2}}\) is one
Hence its degree is one.

Question 4.
\({ \left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 2 }+cos\left( \frac { dy }{ dx } \right) =0\)
Solution:
The highest order derivatives is \(\frac{d^{2} y}{d x^{2}}\)
∴ Order of the equation is 2
The differential equation is not a polynomial equation in its derivatives.
Hence its degree is not defined.

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

Question 5.
\(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } }\) = cos3x + sin3x
Solution:
The highest order derivative is \(\frac{d^{2} y}{d x^{2}}\)
∴ Order is 2
This is a polynomial equation in \(\frac{d^{2} y}{d x^{2}}\) and the power of \(\frac{d^{2} y}{d x^{2}}\) is one
Hence its degree is one.

Question 6.
\({ { (y }^{ ”’ }) }^{ 2 }+{ { ( }y^{ ” }) }^{ 3 }+{ { (y }^{ ‘ }) }^{ 4 }+{ y }^{ 5 }\) = 0
Solution:
The highest order derivative is y”‘
∴ Order is 3
This is a polynomial equation in y”‘, y” and y’ the power of y” is two.
Hence its degree is 2.

Question 7.
y”‘ + 2y” + y’ = 0
Solution:
The highest order derivative is y”‘
∴ Order is 3
This is a polynomial equation in y”‘, y” and y’ and the power of y”‘ is one.
Hence its degree is 1.

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

Question 8.
y’ + y = ex
Solution:
The highest order derivative is y’.
∴ Order is 1
This is a polynomial equation in y’ and the power of y’ is one.
Hence its degree is 1.

Question 9.
y” + (y’) +2y = 0
Solution:
The highest order derivative is y”
∴ Order is 2
This is a polynomial equation in y” and
y’ and the degree of y” is one.
Hence its degree is 1.

Question 10.
y” + 2y’ + sin y = 0
Solution:
The highest order derivative is y”.
∴ Order is 2
This is a polynomial equation in y”, y’ and the power of y” is one.
Hence its degree is 1.

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:
The differential equation is not a polynomial equation in derivatives. Hence the degree is not defined.

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

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:
The highest order derivative is \(\frac{d^{2} y}{d x^{2}}\)
∴ Order is 2.

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