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March 30th, 2012, 01:49 AM   #1
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Reduction of second order ode to first order

Hey,

I've been working on this problem,



I use the hint and end up with a seperable equation then get



after getting p is it correct to integrate p to get y? It doesn't look correct in my working but I can't find another way to do it.

I thought about trying to solve the equation as y'= +/- ... instead as a first order ode but it seems too complicated,

Is there something simple im not seeing?

Thanks in advance
Grayham1990 is offline  
 
March 30th, 2012, 04:50 AM   #2
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Re: Reduction of second order ode to first order

Another way :
y' y = -y''/y'
y/2= (1/y' ) +c
Y(0)=1 ; y'(0) = -1 --> 1/2=-1+c ; c=3/2
y= ('2/y' ) +3
y' = 2/(y-3)
dy/(y-3) = 2 dx
ln[(y-V3)/(y+V3)]/(2V3) = 2x +C
V3 = sqrt(3)
ln[(1-V3)/(1+V3)] /(2V3)= C
ln[(y-V3)/(y+V3)] = 4 V3 x +ln[(1-V3)/(1+V3)]
(y-V3)/(y+V3) = [(1-V3)/(1+V3)]*exp((4 V2) x )
y = ...
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March 30th, 2012, 06:24 AM   #3
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Re: Reduction of second order ode to first order

I just worked on it a little more and got



Just the p formula I wrote in the first post rearranged

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