English

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

Advertisements
Advertisements

Question

Choose the correct option from the given alternatives:

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

Options

  • `"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

Solution

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

shaalaa.com
  Is there an error in this question or solution?
Chapter 6: Differential Equations - Miscellaneous exercise 1 [Page 214]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
Chapter 6 Differential Equations
Miscellaneous exercise 1 | Q 1.02 | Page 214

RELATED QUESTIONS

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

x3 + y3 = 4ax


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


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 = 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 = 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:

`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:

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


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")`


Solve the following differential equation:

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


Choose the correct option from the given alternatives:

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


Choose the correct option from the given alternatives:

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


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" = 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)


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

y = `"Ae"^(3"x" + 1) + "Be"^(- 3"x" + 1)`


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:

x dy = (x + y + 1) 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:

`2e ^(x/y) dx + (y - 2xe^(x/y)) dy = 0," When" y (0) = 1`


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


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


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-horizontal lines in a plane 


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 of all lines perpendicular to the line 5x + 2y + 7 = 0 is ____________.


The differential equation whose solution is (x – h)2 + (y – k)2 = a2 is (where a is a constant) ______.


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 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 for a2y = log x + b, 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.


Solve the differential equation

ex tan y dx + (1 + ex) sec2 y dy = 0


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


The differential equation whose solution represents the family \[x^{2}y=4e^{x}+c\], where c is an arbitrary constant, is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×