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.**

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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.

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.