English

Select and write the correct alternative from the given option for the question General solution of y-xdydx = 0 is

Advertisements
Advertisements

Question

Select and write the correct alternative from the given option for the question

General solution of `y - x ("d"y)/("d"x)` = 0 is

Options

  • `3log x + 7/y` = c

  • `2logx + 3/y` = c

  • log x – log y = log c

  • `3log y + 2/x` = c

MCQ
Advertisements

Solution

log x – log y = log c

shaalaa.com
  Is there an error in this question or solution?
Chapter 2.6: Differential Equations - MCQ

RELATED QUESTIONS

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y2 = (x + c)3


Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y = Ae5x + Be-5x 


Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y = a + `"a"/"x"`


Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y = c1e2x + c2e5x 


Find the differential equation of the ellipse whose major axis is twice its minor axis.


Form the differential equation of all parabolas whose axis is the X-axis.


In the following example verify that the given expression is a solution of the corresponding differential equation:

y = `(sin^-1 "x")^2 + "c"; (1 - "x"^2) ("d"^2"y")/"dx"^2 - "x" "dy"/"dx" = 2`


Solve the following differential equation:

`"dy"/"dx" = (1 + "y")^2/(1 + "x")^2`


Solve the following differential equation:

`"sec"^2 "x" * "tan y"  "dx" + "sec"^2 "y" * "tan x"  "dy" = 0` 


Solve the following differential equation:

cos x . cos y dy − sin x . sin y dx = 0


Solve the following differential equation:

`"dy"/"dx" = - "k",` where k is a constant.


Solve the following differential equation:

`"y"^3 - "dy"/"dx" = "x"^2 "dy"/"dx"`


Solve the following differential equation:

`2"e"^("x + 2y") "dx" - 3"dy" = 0`


For the following differential equation find the particular solution satisfying the given condition:

3ex tan y dx + (1 + ex) sec2 y dy = 0, when x = 0, y = π.


For the following differential equation find the particular solution satisfying the given condition:

`y(1 + log x) dx/dy - x log x = 0, y = e^2,` when x = e


For the following differential equation find the particular solution satisfying the given condition:

`("x" + 1) "dy"/"dx" - 1 = 2"e"^-"y" , "y" = 0`, when x = 1


Reduce the following differential equation to the variable separable form and hence solve:

`"dy"/"dx" = cos("x + y")`


Reduce the following differential equation to the variable separable form and hence solve:

(2x - 2y + 3)dx - (x - y + 1)dy = 0, when x = 0, y = 1.


Solve the following differential equation:

(x2 + y2)dx - 2xy dy = 0


In the following example verify that the given function is a solution of the differential equation.

`"x"^2 + "y"^2 = "r"^2; "x" "dy"/"dx" + "r" sqrt(1 + ("dy"/"dx")^2) = "y"`


Solve the following differential equation:

x dy = (x + y + 1) dx


Solve the following differential equation:

`"dy"/"dx" + "y cot x" = "x"^2 "cot x" + "2x"`


Find the particular solution of the following differential equation:

`("x + 2y"^2) "dy"/"dx" = "y",` when x = 2, y = 1


Find the particular solution of the following differential equation:

(x + y)dy + (x - y)dx = 0; when x = 1 = y


Find the particular solution of the following differential equation:

y(1 + log x) = (log xx) `"dy"/"dx"`, when y(e) = e2


Find the particular solution of the following differential equation:

`2e ^(x/y) dx + (y - 2xe^(x/y)) dy = 0," When" y (0) = 1`


Select and write the correct alternative from the given option for the question

Solution of the equation `x  ("d"y)/("d"x)` = y log y is


Select and write the correct alternative from the given option for the question 

The solutiion of `("d"y)/("d"x) + x^2/y^2` = 0 is


Find the differential equation of family of lines making equal intercepts on coordinate axes


Find the differential equation of the family of all non-horizontal lines in a plane 


Find the differential equation of the family of circles passing through the origin and having their centres on the x-axis


The differential equation of all lines perpendicular to the line 5x + 2y + 7 = 0 is ____________.


The general solution of the differential equation of all circles having centre at A(- 1, 2) is ______.


The elimination of the arbitrary constant m from the equation y = emx gives the differential equation ______.


The differential equation representing the family of parabolas having vertex at origin and axis along positive direction of X-axis is ______.


If m and n are respectively the order and degree of the differential equation of the family of parabolas with focus at the origin and X-axis as its axis, then mn - m + n = ______.


The differential equation for all the straight lines which are at the distance of 2 units from the origin is ______.


Form the differential equation of all lines which makes intercept 3 on x-axis.


Solve the following differential equation:

`xsin(y/x)dy = [ysin(y/x) - x]dx`


The differential equation representing the family of ellipse having foci either on the x-axis or on the y-axis centre at the origin and passing through the point (0, 3) is ______.


If y = (tan–1 x)2 then `(x^2 + 1)^2 (d^2y)/(dx^2) + 2x(x^2 + 1) (dy)/(dx)` = ______.


The differential equation of all parabolas whose axis is Y-axis, is ______.


The differential equation of the family of circles touching Y-axis at the origin is ______.


If 2x = `y^(1/m) + y^(-1/m)`, then show that `(x^2 - 1) (dy/dx)^2` = m2y2


A particle is moving along the X-axis. Its acceleration at time t is proportional to its velocity at that time. Find the differential equation of the motion of the particle.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×