CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Formation of a Differential Equation from a General Solution

Obtain the di...

Question

Obtain the differential equation from the relation $A x^{2} + B y^{2} = 1$ , where A and B are constants.

Open in App

Solution

$A x^{2} + B y^{2} = 1$
By differentiating, we get
$2 A x + 2 B y y_{1} = 0$
$A = - \frac{B y y_{1}}{x}$
$2 A x + 2 B y y_{1} = 0$
By differentiating, we get
$2 A + 2 B y y_{2} + 2 B y_{1}^{2} = 0$
$- B y y_{1} + x (B y y_{2} + B y_{1}^{2}) = 0$
$x y y_{2} + x (y_{1})^{2} - y y_{1} = 0$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Obtain differential equation from the relation

A x^{2} + B y^{2} = 1

, where A and B are constants

Q. The differential equation whose solution is

A x^{2} + B y^{2} = 1

, where A and B are arbitrary constants is of

Q. The differential equation whose solution is

A x^{2} + B y^{2} = 1

A

B

are arbitrary constants is of order and degree respectively:

Q. Form a differential equation for the family of curves represented by

a x^{2} + b y^{2} = 1

, where a & b are arbitary constants.

Q. Form the differential equation by eliminating arbitrary constants from the relation

A x^{2} + B y^{2} = 1

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Formation of Differential Equation

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Formation of a Differential Equation from a General Solution

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon