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

Choose the correct option from the given alternatives: The differential equation of y = ccxc2+cx is

Advertisements
Advertisements

प्रश्न

Choose the correct option from the given alternatives:

The differential equation of y = `"c"^2 + "c"/"x"` is

पर्याय

  • `"x"^4 ("dy"/"dx")^2 - "x" "dy"/"dx" = "y"`

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

  • `"x"^3 ("dy"/"dx")^2 + "x" "dy"/"dx" = "y"`

  • `("d"^2"y")/"dx"^2 + "dy"/"dx" - "y" = 0`

MCQ
Advertisements

उत्तर

`"x"^4 ("dy"/"dx")^2 - "x" "dy"/"dx" = "y"`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Differential Equations - Miscellaneous exercise 1 [पृष्ठ २१४]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 6 Differential Equations
Miscellaneous exercise 1 | Q 1.02 | पृष्ठ २१४

संबंधित प्रश्‍न

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:

c1x3 + c2y2 = 5


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


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


Solve the following differential equation:

`"dy"/"dx" = (1 + "y")^2/(1 + "x")^2`


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:

`"dy"/"dx" = - "k",` where k is a constant.


Solve the following differential equation:

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

`(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:

`cos^2 ("x - 2y") = 1 - 2 "dy"/"dx"`


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


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)


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


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 general solution of `("d"y)/("d"x) = (1 + y^2)/(1 + x^2)`


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


Find the differential equation from the relation x2 + 4y2 = 4b2 


Find the differential equation of the family of all the parabolas with latus rectum 4a and whose axes are parallel to 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 ______.


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


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.


Solve the following differential equation:

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


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 the family of circles touching Y-axis at the origin is ______.


If 2x = `y^(1/m) + y^(-1/m)`, then show that `(x^2 - 1) (dy/dx)^2` = m2y2


Form the differential equation whose general solution is y = a cos 2x + b sin 2x.


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×