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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

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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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पाठ 2.6: Differential Equations - MCQ

संबंधित प्रश्‍न

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

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


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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`


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

y = e-x + Ax + B; `"e"^"x" ("d"^2"y")/"dx"^2 = 1`


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

y = `"e"^"ax"; "x" "dy"/"dx" = "y" log "y"`


Solve the following differential equation:

`log  ("dy"/"dx") = 2"x" + 3"y"`


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


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:

`"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.


Solve the following differential equation:

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


Choose the correct option from the given alternatives:

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Choose the correct option from the given alternatives:

The differential equation of all circles having their centres on the line y = 5 and touching the X-axis is


Choose the correct option from the given alternatives:

The solution of `"dy"/"dx" = ("y" + sqrt("x"^2 - "y"^2))/"x"` is


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Choose the correct option from the given alternatives:

`"x"^2/"a"^2 - "y"^2/"b"^2 = 1` is a solution of


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

`"y"^2 = "a"("b - x")("b + x")`


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.

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


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"`.


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:

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


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


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Find the differential equations of the family of all the ellipses having foci on the y-axis and centre at the origin


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Choose the correct alternative:

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If `x^2 y^2 = sin^-1 sqrt(x^2 + y^2) + cos^-1 sqrt(x^2 + y^2)`, then `"dy"/"dx"` = ?


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


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


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


Solve the differential equation

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Form the differential equation of all concentric circles having centre at the origin.


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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