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 - Mathematics and Statistics

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

उत्तर

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

shaalaa.com
Formation of Differential Equations
  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] 12 Standard HSC 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:

c1x3 + c2y2 = 5


Form the differential equation of all parabolas whose axis is the X-axis.


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` 


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:

`cos("dy"/"dx") = "a", "a" ∈ "R", "y"(0) = 2`


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:

(2x - 2y + 3)dx - (x - y + 1)dy = 0, when x = 0, y = 1.


Choose the correct option from the given alternatives:

x2 + y2 = a2 is a solution of


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.

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


Form the differential equation of all the lines which are normal to the line 3x + 2y + 7 = 0.


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

Solution of the equation `x  ("d"y)/("d"x)` = y log y is


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

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


Find the differential equation by eliminating arbitrary constants from the relation x2 + y2 = 2ax


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 the parabolas with latus rectum 4a and whose axes are parallel to 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


Find the differential equation of the curve represented by xy = aex + be–x + x2


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.


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 ______.


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 parabolas whose axis is Y-axis, 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


Solve the differential equation

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×