The differential equations of all conies whose axes coincide with | Filo
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The differential equations of all conies whose axes coincide with the co-ordinate axis

  1. xyd2ydx2+x(dydx)2+ydydx=0
  2. xyd2ydx2+x(dydx)2+xdydx=0
  3. xyd2ydx2+x(dydx)2−ydydx=0
  4. xyd2ydx2−x(dydx)2+ydydx=0
Correct Answer: Option(c)
Solution: [c] Any conic whose axes coincide with coordinate axis is ax2+by2=1                                   (i) Diff. both sides w.r.t. ′x′, we get 2ax+2bydydx=0 i.e., ax+bydydx=0(ii) Diff. again, a+b(yd2ydx2+(dydx)2)=0(iii) From (ii), ab=−ydy/dxx From (iii), ab=−(yd2ydx2+(dydx)2) ∴ydydxx=yd2ydx2+(dydx)2 ⇒xyd2ydx2+x(dydx)2−ydydx=0
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