(y')^2+y^2=2 why this equation has no general solution ?
hi
(y')^2+y^2=2 why this differential equation has no general solution ? 
Re: (y')^2+y^2=2 why this equation has no general solution ?
It's nonlinear. Having a general solution for these types of equations is the exception, not the rule.
Not that there isn't a general solution because I don't know. It's just that nonlinear equations rarely have general solutions 
Re: (y')^2+y^2=2 why this equation has no general solution ?
Because the lhs is necessarily nonnegative (sum of squares), whereas the lhs is negative. You can have a solution in complex numbers.

Re: (y')^2+y^2=2 why this equation has no general solution ?
Quote:
[tex]\frac{dy}{\sqrt{2y^2}}=\pm dx[/tex] or [itex]y=\pm i\sqrt{2}[/tex] are solutions, maybe singular ones. Not sure. Otherwise: [tex]\frac{y\sqrt{2y^2}}{2+y^2}=\tan(c\pm x)[/tex] [tex]y(x)=\pm \frac{\sqrt{2}\tan(c\pm x)}{\sqrt{\sec^2(c\pm x)}}[/tex] so that the solution is in the form of y(z)=u+iv 
Re: (y')^2+y^2=2 why this equation has no general solution ?
There is no general solution in terms of real valued functions because if y' and y are both real numbers (for a given x) then [itex](y')^2+ y^2[/itex] cannot be negative!
Oops! Dickfore had already said that, hadn't he? 
All times are GMT 5. The time now is 03:48 AM. 
Powered by vBulletin Copyright ©2000  2014, Jelsoft Enterprises Ltd.
© 2014 Physics Forums