# differential equation

• Jan 31st 2009, 09:57 AM
kizler
differential equation
Hi guys i have that (dy/dx)=(y/2x)-(xy)^3

i calculated that the general solution is y=ħsqrt(1/{[(2x^4)/5]+[C/x]})
i used the substitution z=1/y^2
could someone tell me if i got the right solution please?
• Jan 31st 2009, 10:29 AM
Jester
Quote:

Originally Posted by kizler
Hi guys i have that (dy/dx)=(y/2x)-(xy)^3

i calculated that the general solution is y=ħsqrt(1/{[(2x^4)/5]+[C/x]})
i used the substitution z=1/y^2
could someone tell me if i got the right solution please?

It's hard to read your expression but if you got

$\displaystyle y = \pm \frac{1}{\sqrt{\frac{2x^4}{5} + \frac{c}{x}}}$

then yes.
• Jan 31st 2009, 10:31 AM
galactus
It is difficult to read what you have, but if it is equivalent to $\displaystyle y=\pm\sqrt{\frac{5x}{2x^{5}+5C}}$

where $\displaystyle \frac{x}{2x^{5}+5C}\geq 0$, then you are Okey-dokey(Nod)

EDIT: hey, looks like me and big Dan are in the same arena, so I reckon that is it.:)