aivantettet26
  • aivantettet26
Show that the family of circles (x+1)^2+(y-3)^2 = c^2 can be interpreted as two families of solution of the differential equations dy/dx = -(x-1)/y-3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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aivantettet26
  • aivantettet26
\[\frac{ dy }{ dx } = \frac{ -(x+1) }{ y-3 }\]
anonymous
  • anonymous
The proof is as follows. I hope u know Chain Rule and that differentiation is a linear function. Sorry for the picture being a bit hazy.
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IrishBoy123
  • IrishBoy123
you can also solve the DE, it is clearly separable. in fact, that might be much easier as you can complete the square

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anonymous
  • anonymous
yeah... that's an option too... but arranging it into the standard form for a circle would be tedious @IrishBoy123
IrishBoy123
  • IrishBoy123
your choice :p

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