मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Select and write the correct alternative from the given option for the question The solution of dydx = 1 is

Advertisements
Advertisements

प्रश्न

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

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

पर्याय

  • x + y = c

  • xy = c

  • x2 + y2 = c

  • y – x = c

MCQ
Advertisements

उत्तर

y – x = c

shaalaa.com
  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)2 = 4(x - b)


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


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


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 = 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:

`"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.


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


Choose the correct option from the given alternatives:

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


The particular solution of `dy/dx = xe^(y - x)`, when x = y = 0 is ______.


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


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

y = a sin (x + b)


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

(y - a)2 = b(x + 4)


Form the differential equation of all parabolas which have 4b as latus rectum and whose axis is parallel to the Y-axis.


Solve the following differential equation:

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


Solve the following differential equation:

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


Solve the following differential equation:

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


Solve the following differential equation:

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


Solve the following differential equation:

`"dx"/"dy" + "8x" = 5"e"^(- 3"y")`


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


Find the particular solution of the following differential equation:

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


The general solution of `(dy)/(dx)` = e−x is ______.


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


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 all non-horizontal lines in a plane 


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 ______.


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 ______.


The differential equation of all circles passing through the origin and having their centres on the X-axis is ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×