Ask Questions, Get Answers

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

The differential equation $y\Large \frac{dy}{dx}\normalsize+x=c$ represents:\begin{array}{1 1}(A)\;family \;of \;hyperbolas & (B)\;family \;of \;parabolas \\(C)\;family \;of \;ellipses & (D)\;family\; of \;circles\end{array}

Can you answer this question?

1 Answer

0 votes
  • If a linear differential equation is of the type $\large \frac{dy}{dx}$$=f(x)$ then it can be solved by seperating the variables and then integrating
Given $ y \large\frac{dy}{dx}$$+x=c$
This can be written as $y. \large \frac{dy}{dx}$$=-x+c$
Now seperating the variables we get,
$y dy=(-x+c)dx$
Integrating on both sides we get,
$\int ydy=\int (-x+c)dx$
$=> \large\frac{y^2}{2}=\large\frac{-x^2}{2}$$+cx$
Rearranging the terms we get
$=>x^2+y^2-2cx=0\qquad [(x^2-2(x)=(x-c)^2-c^2]$
Clearly this is an equation of a circle with center$(c,0)$ and radius=$c$
Hence the correct option is $D$
answered May 16, 2013 by meena.p

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