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.
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.
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.
Posts
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.....