anonymous
  • anonymous
All lines 1 unit distant from the origin ANS. (xy'-y)^2 = (1 + (y')^2)
Differential Equations
chestercat
  • chestercat
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anonymous
  • anonymous
anonymous
  • anonymous
helo guys
anonymous
  • anonymous
help please

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nincompoop
  • nincompoop
you have multiple post
anonymous
  • anonymous
what is the question here?
anonymous
  • anonymous
Just a guess: Find an ODE whose general solution is the family of curves that satisfy some property. What that property might be, I'm not so sure. "All lines 1 unit distant from the origin" ? idk what to make of that.
anonymous
  • anonymous
well, those are just tangent lines to \(x^2+y^2=1\), so $$2x+2yy'=0\\x+yy'=0\\y'=-\frac{x}y$$so \(\dfrac{dy}{dx}=-\dfrac{x_0}{y_0}\) which gives $$\frac{y-y_0}{x-x_0}=-\frac{x_0}{y_0}$$

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