Determine order and degree(if defined) of differential equation

Determine order and degree(if defined) of differential equation

Determine order and degree(if defined) of differential equation

Determine order and degree(if defined) of differential equation

Determine order and degree(if defined) of differential equation

Determine order and degree(if defined) of differential equation

Determine order and degree(if defined) of differential equation

Determine order and degree(if defined) of differential equation

Determine order and degree(if defined) of differential equation

Determine order and degree(if defined) of differential equation

The degree of the differential equation is (A) 3 (B) 2 (C) 1 (D) not defined

The order of the differential equation is(A) 2 (B) 1 (C) 0 (D) not defined

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

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

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

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

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

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

Formthedifferentialequationofthefamilyofcircleshavingcentreony-axisandradius 3units.

Which of the following differentialequationshasas the generalsolution? A. B. C. D.

Which of the following differentialequationhasas one of its particularsolution? A. B. C. D.

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

For thedifferentialequationfind the solution curvepassing through the point (1,–1).

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.

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).

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.

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_e2 = 0.6931).

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 .

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?

The general solution of the differential equation A. B. C. D.

A homogeneous differential equation oftheformcan be solved by makingthe substitution (I) y =vx (II) v =yx (III) x =vy (IV) x =v

Which of the following is a homogeneous differential equation? A. B. C. D.

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.

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.

The integrating factor of thedifferentialequationis (I) e^–x (II) e^–y C. D. x

The integrating factor of the differential equation. is A. B. C. D.

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

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) (I)

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

Provethatis the general solution ofdifferential equation, where c is aparameter.

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

Find the general solution of the differential equation

Show that the general solution of thedifferentialequationis given by (x + y + 1) = A (1 – x – y – 2xy), where A isparameter

Find the particular solution of the differential equation , given that y = 1 when x = 0

Solve the differential equation

Find a particular solution of thedifferentialequation, giventhat y = – 1, when x = 0 (Hint: put x – y = t)

Solve the differential equation

Find a particular solution of thedifferentialequation, given that y = 0 when

Find a particular solution of thedifferentialequation, given that y =0 when x =0

Thepopulationofavillageincreasescontinuouslyattherateproportionaltothenumber ofitsinhabitantspresentatanytime.Ifthepopulationofthevillagewas20000in1999 and 25000 in the year 2004, what will be the population of the village in2009?

The general solution of thedifferentialequationis (I) xy =C (II) x = Cy² (III) y = Cx (IV) y = Cx2

The general solution of a differential equation of the typeis A. B. C. D.

The general solution of thedifferentialequationis (I) xe^y+ x² =C (II) xe^y+ y² =C (III) ye^x+ x² =C (IV) yey + x2 = C