wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Form the differential equation by eliminating arbitrary constants from the relation Ax2+By2=1 or x2a2+y2b2=1.

Open in App
Solution

Given: Equation of ellipsex2a2+y2b2=1
Concept:
Here we see that there are two arbitrary constants(a and b) in equation of ellipse thus we have to get a differential equation of 2nd order for eliminating all constants.

Solution:
Differentiating given equation with respect to x, we get:
2xa2+2yb2(dydx)=0
yx(dydx)=b2a2

Again differentating with respect to x, we get:
yx(d2ydx2)+xdydxyx2dydx=0

xyd2ydx2+x(dydx)2ydydx=0
which is the required differential equation.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Formation of Differential Equation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon