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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 The solutiion of dydx+x2y2 = 0 is

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प्रश्न

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

पर्याय

  • x3 + y3 = 7

  • x2 + y2 = c

  • x3 + y3 = c

  • x + y = c

MCQ
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उत्तर

x3 + y3 = c

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  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 = a + `"a"/"x"`


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


Find the differential equation of all circles having radius 9 and centre at point (h, k).


Form the differential equation of family of lines parallel to the line 2x + 3y + 4 = 0.


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

xy = log y +c; `"dy"/"dx" = "y"^2/(1 - "xy")`


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 = xm; `"x"^2 ("d"^2"y")/"dx"^2 - "mx" "dy"/"dx" + "my" = 0`


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

y = `"a" + "b"/"x"; "x" ("d"^2"y")/"dx"^2 + 2 "dy"/"dx" = 0`


Solve the following differential equation:

`"y" - "x" "dy"/"dx" = 0`


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:

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


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

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


Solve the following differential equation:

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


Choose the correct option from the given alternatives:

The solution of the differential equation `"dy"/"dx" = sec "x" - "y" tan "x"`


Choose the correct option from the given alternatives:

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


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"`


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

`"y" = "e"^"ax" sin "bx"; ("d"^2"y")/"dx"^2 - 2"a" "dy"/"dx" + ("a"^2 + "b"^2)"y" = 0`


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`


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 = a sin (x + b)


Solve the following differential equation:

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


Solve the following differential equation:

x dy = (x + y + 1) dx


Solve the following differential equation:

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


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


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

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


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

The solution of `("d"y)/("d"x)` = 1 is


Find the differential equation of family of all ellipse whose major axis is twice the minor axis


The differential equation having y = (cos-1 x)2 + P (sin-1 x) + Q as its general solution, where P and Q are arbitrary constants, is 


Find the differential equation of the family of all non-vertical 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


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


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 ______.


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 circles passing through the origin and having their centres on the X-axis is ______.


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


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