The general solution of the differential equation is
A. xey + x2 = C
B. xey + y2 = C
C. yex + x2 = C
D. yey+ x2 = C
Uploaded bysandeep View Answer
The general solution of a differential equation of the type is
A.
B.
C.
D.
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?
Find a particular solution of the differential equation, given that y = 0 when x = 0
Find a particular solution of the differential equation , given that y = 0 when
Solve the differential equation
Find a particular solution of the differential equation, given that y = – 1, when x = 0 (Hint: put x– y = t)
Find the particular solution of the differential equation
, given that y = 1 when x = 0
Find the equation of the curve passing through the point whose differential equation is,
Show that the general solution of the differential equation is given by (x + y + 1) = A (1 – x – y – 2xy), where A is parameter
Find the general solution of the differential equation
Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.
Prove that is the general solution of differential equation, where c is a parameter.
Form the differential equation representing the family of curves given by where a is an arbitrary constant.
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)
For each of the differential equations given below, indicate its order and degree (if defined).
The integrating factor of the differential equation.
is
The integrating factor of the differential equation is
A. e–x
B. e–y
D. x
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.
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.
Which of the following is a homogeneous differential equation?
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
:
The general solution of the differential equation
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 bank, principal increases continuously at the rate of r% per year. Find the value of r if Rs 100 doubles itself in 10 years (loge 2 = 0.6931).
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.
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)
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.
For the differential equation find the solution curve passing through the point (1, –1).
Find the equation of a curve passing through the point (0, 0) and whose differential equation is.
Which of the following differential equation hasas one of its particular solution?
Which of the following differential equations hasas the general solution?
Form the differential equation of the family of circles having centre on y-axis and radius 3 units.
Form the differential equation of the family of hyperbolas having foci on x-axis and centre at origin.
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 parabolas having vertex at origin and axis along positive y-axis.
Form the differential equation of the family of circles touching the y-axis at the origin.
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
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 order of the differential equation
(A) 2 (B) 1 (C) 0 (D) not defined
he degree of the differential equation
(A) 3 (B) 2 (C) 1 (D) not defined
Determine order and degree(if defined) of differential equation