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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

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

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प्रश्न

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

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

पर्याय

  • `3log x + 7/y` = c

  • `2logx + 3/y` = c

  • log x – log y = log c

  • `3log y + 2/x` = c

MCQ

उत्तर

log x – log y = log c

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Formation of Differential Equations
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2.6: Differential Equations - MCQ

संबंधित प्रश्‍न

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

x3 + y3 = 4ax


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

y = A cos (log x) + B sin (log x)


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

y = e−2x (A cos x + B sin x)


Form the differential equation of family of lines having intercepts a and b on the co-ordinate ares respectively.


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

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


Solve the following differential equation:

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


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


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

`cos("dy"/"dx") = "a", "a" ∈ "R", "y"(0) = 2`


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

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


The integrating factor of linear differential equation `x dy/dx + 2y = x^2 log x` is ______.


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

`"x"^2 = "2y"^2 log "y",  "x"^2 + "y"^2 = "xy" "dx"/"dy"`


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

y = `sqrt("a" cos (log "x") + "b" sin (log "x"))`


Solve the following differential equation:

x dy = (x + y + 1) dx


Find the particular solution of the following differential equation:

`"dy"/"dx" - 3"y" cot "x" = sin "2x"`, when `"y"(pi/2) = 2`


Find the particular solution of the following differential equation:

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


Form the differential equation of y = (c1 + c2)ex 


Verify y = log x + c is the solution of differential equation `x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0


The family of curves y = `e^("a" sin x)`, where a is an arbitrary constant, is represented by the differential equation.


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


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


Form the differential equation of all straight lines touching the circle x2 + y2 = r2


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


The rate of disintegration of a radio active element at time t is proportional to its mass, at the time. Then the time during which the original mass of 1.5 gm. Will disintegrate into its mass of 0.5 gm. is proportional to ______.


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 ______.


For the curve C: (x2 + y2 – 3) + (x2 – y2 – 1)5 = 0, the value of 3y' – y3 y", at the point (α, α), α < 0, on C, is equal to ______.


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 ______.


Find the particular solution of the differential equation `x^2 dy/dx + y^2 = xy dy/dx`, if y = 1 when x = 1.


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