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**Exercise 9.1 : ** Solutions of Questions on Page Number : **382**

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**Exercise 9.2 : ** Solutions of Questions on Page Number : **385**

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**Exercise 9.3 : ** Solutions of Questions on Page Number : **391**

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**Exercise 9.4 : ** Solutions of Questions on Page Number : **395**

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**Exercise 9.5 : ** Solutions of Questions on Page Number : **406**

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**Exercise 9.6 : ** Solutions of Questions on Page Number : **413**

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**Exercise Miscellaneous : ** Solutions of Questions on Page Number : **419**

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**Popular Articles**

Q1 :
**
**

Determine order and degree(if defined) of differential equation

**Answer :**

The highest order derivative present in the differential equation is. Therefore, its order is four.

The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined.

Answer needs Correction? Click Here

Q2 :
**
**

Determine order and degree(if defined) of differential equation

**Answer :**

The given differential equation is:

The highest order derivative present in the differential equation is. Therefore, its order is one.

It is a polynomial equation in. The highest power raised tois 1. Hence, its degree is one.

Answer needs Correction? Click Here

Q3 :
**
**

Determine order and degree(if defined) of differential equation

**Answer :**

Q4 :
**
**

Determine order and degree(if defined) of differential equation

**Answer :**

Q5 :
**
**

Determine order and degree(if defined) of differential equation

**Answer :**

Q6 :
**
**

Determine order and degree(if defined) of differential equation

**Answer :**

Q7 :
**
**

Determine order and degree(if defined) of differential equation

**Answer :**

Q8 :
**
**

Determine order and degree(if defined) of differential equation

**Answer :**

Q9 :
**
**

Determine order and degree(if defined) of differential equation

**Answer :**

Q10 :
**
**

Determine order and degree(if defined) of differential equation

**Answer :**

Q11 :
**
**

The degree of the differential equation

is

**(A)** 3 **(B)** 2 **(C)** 1 **(D)** not defined

**Answer :**

Q12 :
**
**

The order of the differential equation

is

**(A)** 2 **(B)** 1 **(C)** 0 **(D)** not defined

**Answer :**

Q11 :
**
**

The numbers of arbitrary constants in the general solution of a differential equation of fourth order are:

**(A)** 0 **(B)** 2 **(C)** 3 **(D)** 4

**Answer :**

Q12 :
**
**

The numbers of arbitrary constants in the particular solution of a differential equation of third order are:

(A) 3 (B) 2 (C) 1 (D) 0

**Answer :**

Q6 :
**
**

Form the differential equation of the family of circles touching
the *y*-axis at the origin.

**Answer :**

Q7 :
**
**

Form the differential equation of the family of parabolas having
vertex at origin and axis along positive *y*-axis.

**Answer :**

Q8 :
**
**

Form the differential equation of the family of ellipses having
foci on *y*-axis and centre at origin.

**Answer :**

Q9 :
**
**

Form the differential equation of the family of hyperbolas having
foci on *x*-axis and centre at origin.

**Answer :**

Q10 :
**
**

Form the differential equation of the family of circles having
centre on *y*-axis and radius 3 units.

**Answer :**

Q11 :
**
**

Which of the following differential equations hasas the general solution?

**A.**

**B.**

**C.**

**D.**

**Answer :**

Q12 :
**
**

Which of the following differential equation hasas one of its particular solution?

**A.**

**B.**

**C.**

**D.**

**Answer :**

Q15 :
**
**

Find the equation of a curve passing through the point (0, 0) and whose differential equation is.

**Answer :**

Q16 :
**
**

For the differential equation find the solution curve passing through the point (1, â€“1).

**Answer :**

Q17 :
**
**

Find the equation of a curve passing through the point (0,
â€“2) given that at any point on the curve, the
product of the slope of its tangent and *y*-coordinate of
the point is equal to the *x*-coordinate of the point.

**Answer :**

Q18 :
**
**

At any point (*x*, *y*) of a curve, the slope of the
tangent is twice the slope of the line segment joining the point
of contact to the point (-4,
-3). Find the equation of the curve given
that it passes through (-2, 1).

**Answer :**

Q19 :
**
**

The volume of spherical balloon being inflated changes at a
constant rate. If initially its radius is 3 units and after 3
seconds it is 6 units. Find the radius of balloon after *t*
seconds.

**Answer :**

Q20 :
**
**

In a bank, principal increases continuously at the rate of
*r*% per year. Find the value of *r* if Rs 100 doubles
itself in 10 years
(log_{e} 2 = 0.6931).

**Answer :**

Q21 :
**
**

In a bank, principal increases continuously at the rate of 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years.

**Answer :**

Q22 :
**
**

In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria is proportional to the number present?

**Answer :**

Q23 :
**
**

The general solution of the differential equation

**A.**

**B.**

**C.**

**D. **

**Answer :**

Q16 :
**
**

A homogeneous differential equation of the form can be solved by making the substitution

**A.** *y* = *vx*

**B.** *v* = *yx*

**C.** *x* = *vy*

**D.** *x* = *v*

**Answer :**

Q17 :
**
**

Which of the following is a homogeneous differential equation?

**A.**

**B.**

**C.**

**D.**

**Answer :**

Q15 :
**
**

Find the equation of a curve passing through the origin given
that the slope of the tangent to the curve at any point
(*x*, *y*) is equal to the sum of the coordinates of
the point.

**Answer :**

Q16 :
**
**

Find the equation of a curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.

**Answer :**

Q17 :
**
**

The integrating factor of the differential equation is

**A.**
*e*^{â€“}^{x}

**B.**
*e*^{â€“}^{y}

**C.**

**D.** *x*

**Answer :**

Q18 :
**
**

The integrating factor of the differential equation.

is

**A.**

**B.**

**C.**

**D.**

**Answer :**

Q1 :
**
**

For each of the differential equations given below, indicate its order and degree (if defined).

**(i)**

**(ii)**

**(iii)**

**Answer :**

Q2 :
**
**

For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.

**(i)**

**(ii)**

**(iii)**

**(iv)**

**Answer :**

Q3 :
**
**

Form the differential equation representing the family of curves
given by where *a* is an
arbitrary constant.

**Answer :**

Q4 :
**
**

Prove that is the general solution
of differential equation, where *c* is a
parameter.

**Answer :**

Q5 :
**
**

Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.

**Answer :**

Q6 :
**
**

Find the general solution of the differential equation

**Answer :**

Q7 :
**
**

Show that the general solution of the differential equation
is given by (*x* +
*y* + 1) = *A* (1 â€“ *x*
â€“ *y* â€“ 2*xy*),
where *A* is parameter

**Answer :**

Q8 :
**
**

Find the equation of the curve passing through the point whose differential equation is,

**Answer :**

Q9 :
**
**

Find the particular solution of the differential equation

, given that *y* =
1 when *x* = 0

**Answer :**

Q10 :
**
**

Solve the differential equation

**Answer :**

Q11 :
**
**

Find a particular solution of the differential equation, given that *y* =
â€“ 1, when *x* = 0 (Hint: put *x*
â€“ *y* = *t*)

**Answer :**

Q12 :
**
**

Solve the differential equation

**Answer :**

Q13 :
**
**

Find a particular solution of the differential equation
, given that *y* =
0 when

**Answer :**

Q14 :
**
**

Find a particular solution of the differential equation, given that *y* =
0 when *x* = 0

**Answer :**

Q15 :
**
**

The population of a village increases continuously at the rate proportional to the number of its inhabitants present at any time. If the population of the village was 20000 in 1999 and 25000 in the year 2004, what will be the population of the village in 2009?

**Answer :**

Q16 :
**
**

The general solution of the differential equation is

**A.** *xy* = C

**B.** *x* = C*y*^{2}

**C.** *y* = C*x*

**D.** *y* = C*x*^{2}

**Answer :**

Q17 :
**
**

The general solution of a differential equation of the type is

**A.**

**B.**

**C.**

**D. **

**Answer :**

Q18 :
**
**

The general solution of the differential equation is

**A.** *xe*^{y} + *x*^{2} = C

**B.** *xe*^{y} + *y*^{2} = C

**C.** *ye*^{x} + *x*^{2} = C

**D.** *ye*^{y}+ *x*^{2} = C

**Answer :**

Maths Part-2 - Maths : CBSE ** NCERT ** Exercise Solutions for Class 12th for ** Differential Equations ** ( Exercise 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

- 12th Maths Paper Solutions Set 1 : CBSE Delhi Previous Year 2015
- 12th Maths Paper Solutions Set 2 : CBSE Delhi Previous Year 2015
- 12th Maths Paper Solutions Set 3 : CBSE Delhi Previous Year 2015

- 12th Maths Paper Solutions Set 1 : CBSE Abroad Previous Year 2014
- 12th Maths Paper Solutions Set 1 : CBSE All India Previous Year 2014
- 12th Maths Paper Solutions Set 1 : CBSE Delhi Previous Year 2014

- 12th Maths Paper Solutions Set 1 : CBSE All India Previous Year 2013

- Maths Part-1 : Chapter 5 - Continuity and Differentiability Class 12
- Maths Part-1 : Chapter 6 - Application of Derivatives Class 12
- Maths Part-2 : Chapter 7 - Integrals Class 12
- Maths Part-1 : Chapter 1 - Relations and Functions Class 12
- Maths Part-1 : Chapter 3 - Matrices Class 12
- Maths Part-1 : Chapter 4 - Determinants Class 12
- Maths Part-1 : Chapter 2 - Inverse Trigonometric Functions Class 12
- Maths Part-2 : Chapter 13 - Probability Class 12
- Maths Part-2 : Chapter 8 - Application of Integrals Class 12

Exercise 9.1 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |

Question 11 |

Question 12 |

Exercise 9.2 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |

Question 11 |

Question 12 |

Exercise 9.3 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |

Question 11 |

Question 12 |