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March 30th, 2012, 01:49 AM  #1 
Member Joined: Nov 2011 Posts: 40 Thanks: 0  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 
March 30th, 2012, 04:50 AM  #2 
Senior Member Joined: Aug 2011 Posts: 334 Thanks: 8  Re: Reduction of second order ode to first order
Another way : y' y = y''/y'² y²/2= (1/y' ) +c Y(0)=1 ; y'(0) = 1 > 1/2=1+c ; c=3/2 y²= ('2/y' ) +3 y' = 2/(y²3) dy/(y²3) = 2 dx ln[(yV3)/(y+V3)]/(2V3) = 2x +C V3 = sqrt(3) ln[(1V3)/(1+V3)] /(2V3)= C ln[(yV3)/(y+V3)] = 4 V3 x +ln[(1V3)/(1+V3)] (yV3)/(y+V3) = [(1V3)/(1+V3)]*exp((4 V2) x ) y = ... 
March 30th, 2012, 06:24 AM  #3 
Member Joined: Nov 2011 Posts: 40 Thanks: 0  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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ode, order, reduction 
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