What might be a solution to the differential equation of the form $$xy''=c{y\over y+d}$$ where $y=y(x)$ and $c,d $ are constants? I am supposed to simply "state" a solution to this, but I don;t think it is all that obvious.
A Second order ODE
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ordinary-differential-equations
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0Not obvious at all, unless you're allowed to use the trivial solution $y=0$. Are there any boundary conditions? – 2012-03-26
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0Well, $y(x)=0$ is a solution of your ODE. – 2012-03-26
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0@Pacciu: Yes, I saw that too :) But I don't think that is what they are after...! – 2012-03-26
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0@in_wolfram_we_trust: (Nice username name!) The boundary conditions would be $y'(0)=0$, and $x(0)=x_0$. Sorry for omitting them earlier, I just thought I could plug them in after "spotting" the general solution. – 2012-03-26
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0For clarity: by $x(0)=x_{0}$ do you mean that $x$ is a function of some other variable, say $t$, and $y = y(x(t))$? – 2012-03-26