English

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

Advertisements
Advertisements

Question

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

Sum
Advertisements

Solution

x2 + 4y2 = 4b2      ......(i)

Here, b is an arbitrary constant.

Differentiating w.r.t. x, we get

`2x + 4(2y  ("d"y)/("d"x))` = 0

∴ `x + 4y ("d"y)/("d"x)` = 0

shaalaa.com
  Is there an error in this question or solution?
Chapter 2.6: Differential Equations - Attempt the following questions III

APPEARS IN

SCERT Maharashtra Mathematics and Statistics (Arts and Science) [English] Standard 12 Maharashtra State Board
Chapter 2.6 Differential Equations
Attempt the following questions III | Q 3

RELATED QUESTIONS

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

Ax2 + By2 = 1


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

y2 = (x + c)3


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


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


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`


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:

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


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:

`(e^y + 1) cos x + e^y sin x. dy/dx = 0,  "when" x = pi/6,` y = 0


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

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


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.

`"xy" = "ae"^"x" + "be"^-"x" + "x"^2; "x" ("d"^2"y")/"dx"^2 + 2 "dy"/"dx" + "x"^2 = "xy" + 2`


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:

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


Solve the following differential equation:

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


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 solutiion of `("d"y)/("d"x) + x^2/y^2` = 0 is


Form the differential equation of family of standard circle


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 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 general solution of the differential equation of all circles having centre at A(- 1, 2) is ______.


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


The differential equation of all parabolas having vertex at the origin and axis along positive 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


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


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×