Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Differential Equations
0 votes

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.$y^2=a(b^2-x^2)$

Can you answer this question?

1 Answer

0 votes
  • Product Rule: Differentiating a function which is in the form of product is $uv = uv' +vu'$
Step 1:
Given : $y^2 = a(b^2 - x^2)$
Differenting with respect to $x$ on both sides we get
$2yy' = -2ax$
Dividing on both sides by $-2$ we get,
$yy' = -ax$ ---------(1)
Step 2:
Differenting once again on both sides:
Using the information in the tool box we use product rule to differentiate yy'.
Let $y = u$ and $v = y'$. Hence $u' = y'$ and $v' = y''$
Applying this to differentiate equ (1) we get
$yy'' + y'.y' = -a$
$yy'' + (y')^2 = -a$ -------(2)
Step 3:
Dividing equ (2) by (1) we get
$\large\frac{[yy'' + (y')^2 = -a]}{[yy' = -ax]}$
We get $\large\frac{[yy'' + (y')^2]}{ yy' }=\frac{ 1}{x}$
on cross multiplying and rearranging we get
$xyy'' + x(y')^2 -yy'' = 0.$
answered Aug 16, 2013 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App