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Nonlinear ODEs (My notes at back at school!)
Akilae729
Registered User regular
Registered User regular
Does any one recognize this type of function? (more importantly does it have a name?)
y" + (y')^2 = 0?
It's the last step of a homework problem and I know that the solution is x = ln(x+c1)+c2 (based on what I have to match my solution to)
I can just look this up tomorrow after work when I get back in LA, but I'd like to put this assignment to bed tonight and don't have my Diff Eq notes with me.
y" + (y')^2 = 0?
It's the last step of a homework problem and I know that the solution is x = ln(x+c1)+c2 (based on what I have to match my solution to)
I can just look this up tomorrow after work when I get back in LA, but I'd like to put this assignment to bed tonight and don't have my Diff Eq notes with me.
Akilae729 on
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These are usually a bitch. You make a change of variables and hope for the best.
Lucky for you the details for your equation are here:
http://www.sosmath.com/diffeq/second/nonlineareq/nonlineareq.html
The only difference between this and a first-order linear DE, is that instead the order is one degree higher; however - as was mentioned above - you can make a change of variables where y" becomes z', and y' becomes z. Then you have a first order DE (in z), and from here its just a matter of figuring out the integrating factor, etc. etc.
The only change is that you will have to do this TWICE. . .will leave that to you.
I vaguely remembered the change of variables.....