Help! I'm just starting this class and I have no idea what's going on. What I don't understand is, what answer are you supposed to give? My question says "Find the general solution and also the singular solution, if it exists". What the hell does that mean?(adsbygoogle = window.adsbygoogle || []).push({});

Can someone tell me if this is right?

Question: [tex]x(y')^2 - (2x + 3y)y' + 6y = 0[/tex]

so let [tex]p = y'[/tex]

[tex]xp^2 - (2x + 3y)p + 6y = 0[/tex]

[tex]xp^2 - 2xp - 3yp + 6y = 0[/tex]

[tex]-3yp + 6y = -xp^2 + 2xp[/tex]

[tex]y = \frac{(-xp)(p-2)}{(-3)(p-2)}[/tex]

[tex]y = \frac{xp}{3} [/tex]

so then,

[tex]3y' = 3p = xp' + p[/tex]

[tex]2p = xp'[/tex]

[tex]2p = x \frac{dp}{dx}[/tex]

[tex]\frac{dp}{p} = 2\frac{dx}{x}[/tex]

[tex]\ln{P} = 2\ln{x} + \ln{C}[/tex]

[tex]p = cx^2[/tex]

[tex]y' = cx^2[/tex]

[tex]y = cx^3 + b[/tex], where c and b are constants

and that's as far as I got...now what?

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# Reducing 2nd order to 1st order type question

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