**Question 1**

Determine order and degree(if defined) of differential equation

**Question 2**

Determine order and degree(if defined) of differential equation

**Question 3**

Determine order and degree(if defined) of differential equation

**Question 4**

Determine order and degree(if defined) of differential equation

**Question 5**

Determine order and degree(if defined) of differential equation

**Question 6**

Determine order and degree(if defined) of differential equation

**Question 7**

Determine order and degree(if defined) of differential equation

**Question 8**

Determine order and degree(if defined) of differential equation

**Question 9**

The degree of the differential equation

is

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

**Question 10**

The order of the differential equation

is

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

**Question 11**

Determine order and degree(if defined) of differential equation

**Question 12**

Determine order and degree(if defined) of differential equation

**Question 13**

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

**(i)**

**(ii)**

**(iii)**

**Question 14**

**Question 15**

**Question 16**

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

**Question 17**

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

**Question 18**

**Question 19**

**Question 20**

**Question 21**

**Question 22**

**Question 23**

**Question 24**

**Question 25**

**Question 26**

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

**A.**

**B.**

**C.**

**D.**

**Question 27**

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)**

**Question 28**

**Question 29**

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

**Question 30**

Which of the following differential equations hasas the general solution?

**A.**

**B.**

**C.**

**D.**

**Question 31**

**Question 32**

**Question 33**

**Question 34**

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

**Question 35**

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

**Question 36**

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

**Question 37**

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

**Question 38**

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

**Question 39**

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

**Question 40**

**Question 41**

**Question 42**

**Question 43**

**Question 44**

**Question 45**

**Question 46**

**Question 47**

**Question 48**

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

**Question 49**

For the differential equation find the solution curve passing through the point (1, –1).

**Question 50**

Find the equation of a curve passing through the point (0, –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.

**Question 51**

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).

**Question 52**

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.

**Question 53**

**Question 54**

**Question 55**

**Question 56**

**Question 57**

**Question 58**

**Question 59**

**Question 60**

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).

**Question 61**

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.

**Question 62**

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?

**Question 63**

The general solution of the differential equation

**A.**

**B.**

**C.**

**D. **

**Question 64**

Solve the differential equation

**Question 65**

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

**Question 66**

Find the general solution of the differential equation

**Question 67**

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

**Question 68**

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

**Question 69**

Find the particular solution of the differential equation

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

**Question 70**

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?

**Question 71**

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}

**Question 72**

**Question 73**

**Question 74**

**Question 75**

**Question 76**

**Question 77**

**Question 78**

**Question 79**

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*

**Question 80**

**Question 81**

**Question 82**

**Question 83**

**Question 84**

**Question 85**

**Question 86**

**Question 87**

**Question 88**

Which of the following is a homogeneous differential equation?

**A.**

**B.**

**C.**

**D. **

**Question 89**

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

**Question 90**

**Question 91**

**Question 92**

**Question 93**

**Question 94**

**Question 95**

**Question 96**

**Question 97**

**Question 98**

**Question 99**

**Question 100**

**Question 101**

**Question 102**

**Question 103**

**Question 104**

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.

**Question 105**

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.

**Question 106**

The integrating factor of the differential equation is

**A.** *e*^{–}^{x}

**B.** *e*^{–}^{y}

**C.**

**D. ***x*

**Question 107**

The integrating factor of the differential equation.

is

**A.**

**B.**

**C.**

**D.**

**Question 108**

**Question 109**

Solve the differential equation

**Question 110**

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

**Question 111**

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

**Question 112**

The general solution of a differential equation of the type is

**A.**

**B.**

**C.**

**D. **

**Question 113**

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

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