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anonymous
 one year ago
all lines whose slopes and x intecept equal Ans. y=y'xy'^2
anonymous
 one year ago
all lines whose slopes and x intecept equal Ans. y=y'xy'^2

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Any linear function takes the form \(y=mx+b\), where \(m\) is the slope and \(b\) is the intercept. Fix \(m=b\), then take your derivatives. \[y=m(x+1)~~\implies~~y'=m\] Backsubstituting, you see that \[y=y'(x+1)=y'x+y'\] will work. I don't see a reason to have \((y')^2\) there... Just to check that this is indeed a sufficient ODE, let's solve it: \[y=y'x+y'~~\iff~~y=(x+1)\frac{dy}{dx}~~\implies~~\frac{dy}{y}=\frac{dx}{x+1}\] Integrating yields \[\ln y=\lnx+1+C=\lnx+1+\lnC=\lnC(x+1)~~\implies~~y=C(x+1)\] where \(C=m\).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The given solution seems more along the lines of the ODE whose solutions are all lines \(y=mx+b\) with \(b=m^2\).
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