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The differential equation ydydx+x=c  represents:

(A) Family of hyperbolas

(B) Family of parabolas

(C) Family of ellipses

(D) Family of circles

0 2 Views | Posted 3 months ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    3 months ago

    This is an Objective Type Questions as classified in NCERT Exemplar

    Sol:

    The  given  Differential  equation  is  ydydx+x=c⇒                ydydx=c−x         ydy=(c−x)dx∴Integrating  both  sides,  we  get⇒             ∫ydy=∫(c−x)dx⇒                  y22=cx−x22+k⇒                  x22+y22−cx=k⇒                  x2+y2−2cx=2k  which  is  a  family  of  circles.Hence,  the  correct  option  is  (d).

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