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:

x3 + y3 = 4ax


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

y2 = (x + c)3


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

c1x3 + c2y2 = 5


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

y = e−2x (A cos x + B sin x)


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.


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


Form the differential equation of family of lines parallel to the line 2x + 3y + 4 = 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`


In the following example verify that the given expression is a solution of the corresponding differential equation:

y = `"e"^"ax"; "x" "dy"/"dx" = "y" log "y"`


Solve the following differential equation:

`"y"^3 - "dy"/"dx" = "x"^2 "dy"/"dx"`


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`


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

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


Choose the correct option from the given alternatives:

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


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"`


Choose the correct option from the given alternatives:

`"x"^2/"a"^2 - "y"^2/"b"^2 = 1` is a solution of


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

y = a sin (x + b)


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"`


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 ______.


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


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


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


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 parabolas with vertex at (0, –1) and having axis along the y-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 ______.


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


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 of all circles passing through the origin and having their centres on the X-axis 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.


Solve the differential equation

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


A particle is moving along the X-axis. Its acceleration at time t is proportional to its velocity at that time. Find the differential equation of the motion of the particle.


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×