Differential Equations

**sinichko** · May 8th 2010, 09:48 AM

Please help me solve:

1. $y'(1+y'^{2})=ay''$

2. $y^{3}y''=1$

3. $xy''=y'ln\frac{y'}{x}$

**Krizalid** · May 8th 2010, 11:04 AM

1 and 3 are reduced to first order by putting $t=y'.$

**mr fantastic** · May 8th 2010, 03:00 PM

Originally Posted by sinichko

Please help me solve:
[snip]

2. $y^{3}y''=1$

[snip]

$\frac{d^2y}{dx^2} = \frac{1}{y^3}$ is solved by first making the substitution $\frac{d^2 y}{dx^2} = \frac{d}{dy}\left[ \frac{v^2}{2}\right]$ where $v = \frac{dy}{dx}$ and solving for v.

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