मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

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

Advertisements
Advertisements

प्रश्न

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

बेरीज
Advertisements

उत्तर

Given relation is

x2 + 4y2 = 4b2

Differentiating w.r.t. x, we get

`2x + 4.2y ("d"y)/("d"x) = 0`

∴ `x + 4y ("d"y)/("d"x)  = 0`, which is the required differential equation.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.8: Differential Equation and Applications - Q.5

संबंधित प्रश्‍न

Verify that y = 4 sin 3x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + 9y = 0\]


\[\frac{dy}{dx} = \frac{1 - \cos x}{1 + \cos x}\]

\[\sin^4 x\frac{dy}{dx} = \cos x\]

xy dy = (y − 1) (x + 1) dx


\[\frac{dy}{dx} = e^{x + y} + e^y x^3\]

dy + (x + 1) (y + 1) dx = 0


Solve the differential equation \[\left( 1 + x^2 \right)\frac{dy}{dx} + \left( 1 + y^2 \right) = 0\], given that y = 1, when x = 0.


Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\]  given that y = 1, when x = 0.


\[\frac{dy}{dx} = \frac{\left( x - y \right) + 3}{2\left( x - y \right) + 5}\]

\[\left( x + y \right)^2 \frac{dy}{dx} = 1\]

\[\frac{dy}{dx} = \frac{y^2 - x^2}{2xy}\]

Solve the following initial value problem:-

\[\frac{dy}{dx} - 3y \cot x = \sin 2x; y = 2\text{ when }x = \frac{\pi}{2}\]


The surface area of a balloon being inflated, changes at a rate proportional to time t. If initially its radius is 1 unit and after 3 seconds it is 2 units, find the radius after time t.


The slope of the tangent at a point P (x, y) on a curve is \[\frac{- x}{y}\]. If the curve passes through the point (3, −4), find the equation of the curve.


Find the equation of the curve which passes through the point (1, 2) and the distance between the foot of the ordinate of the point of contact and the point of intersection of the tangent with x-axis is twice the abscissa of the point of contact.


Radium decomposes at a rate proportional to the quantity of radium present. It is found that in 25 years, approximately 1.1% of a certain quantity of radium has decomposed. Determine approximately how long it will take for one-half of the original amount of  radium to decompose?


The x-intercept of the tangent line to a curve is equal to the ordinate of the point of contact. Find the particular curve through the point (1, 1).


The solution of the differential equation y1 y3 = y22 is


Solve the differential equation:

`e^(dy/dx) = x`


x2y dx – (x3 + y3) dy = 0


 `dy/dx = log x`


Solve the following differential equation

`x^2  ("d"y)/("d"x)` = x2 + xy − y2 


Choose the correct alternative:

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


Choose the correct alternative:

Differential equation of the function c + 4yx = 0 is


The solution of differential equation `x^2 ("d"^2y)/("d"x^2)` = 1 is ______


The function y = cx is the solution of differential equation `("d"y)/("d"x) = y/x`


What distinguishes an ordinary differential equation from other types of differential equations?


In mathematics and science, what primary purpose do differential equations serve?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×