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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
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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:

y = e−2x (A cos x + B sin x)


Find the differential equation all parabolas having a length of latus rectum 4a and axis is parallel to the axis.


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:

`"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^2y)/x dy + (cos^2x)/y dx` = 0


Solve the following differential equation:

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


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:

`(e^y + 1) cos x + e^y sin x. dy/dx = 0,  "when" x = pi/6,` y = 0


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:

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


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.


Choose the correct option from the given alternatives:

The solution of `"dy"/"dx" + "y" = cos "x" - sin "x"`


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.

`"y" = 3 "cos" (log "x") + 4 sin (log "x"); "x"^2 ("d"^2"y")/"dx"^2 + "x" "dy"/"dx" + "y" = 0`


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

`"xy" = "ae"^"x" + "be"^-"x" + "x"^2; "x" ("d"^2"y")/"dx"^2 + 2 "dy"/"dx" + "x"^2 = "xy" + 2`


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

y = a sin (x + b)


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

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Form the differential equation of the hyperbola whose length of transverse and conjugate axes are half of that of the given hyperbola `"x"^2/16 - "y"^2/36 = "k"`.


Solve the following differential equation:

y log y = (log y2 - x) `"dy"/"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:

`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

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


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


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


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 ______.


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 ______.


The differential equation of all parabolas having vertex at the origin and axis along positive Y-axis is ______.


Solve the differential equation

cos2(x – 2y) = `1 - 2dy/dx`


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


Solve the differential equation

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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.


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