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Number 65 in http://www.math.ucsb.edu/mathclub/GRE/GRE8767.pdf asks to find the graphs possible curves that satisfy the differential equation

$(\frac{dy}{dx})^2 + 2y \frac{dy}{dx} + y^2 = 0$

What method is used to solve this differential equation?

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up vote 8 down vote accepted

The given equation can be rewritten as: $$ \left( \frac{dy}{dx} + y \right)^2 = 0. $$

You should be able to go from here, assuming you know how to solve first order linear differential equations. I don't want to spoil the fun too much! :-)

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Why community wiki? Why not accept credit where credit is due? –  Gerry Myerson Oct 12 '11 at 5:07
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@Gerry The official reason is that it seemed too simple (plus, I didn't want to give out the full answer). For the actual reason, please take a look at my reputation points. I am trying to enjoy it while it lasts. :-) –  Srivatsan Oct 12 '11 at 5:10
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Well, but the more credit you accept, the quicker you'll get to 6666. –  Gerry Myerson Oct 12 '11 at 6:10
    
@Gerry I see your point. In fact, after writing that comment, I felt guilty of being frivolous, so I wrote an answer to some other question so that I could 'move on' :). Thanks for the push anyway. –  Srivatsan Oct 12 '11 at 6:27
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