Use the substiution y=xu to find the general solution of the differential equation:
(x+y)dy/dx=y
dy/dx = u+x(du/dx)
(x+xu)(u+x(du/dx)=xu
where do i go from here?
thanks
I would bet he/she is making the substitution because
BabyMilo,
$\displaystyle (x+xu)dy-xudx=0$
$\displaystyle dy=udx+xdu$
$\displaystyle (x+xu)(udx+xdu)-xudx=0\Rightarrow x(1+u)(udx+xdu)-xudx=0$
$\displaystyle \Rightarrow (1+u)(udx+xdu)-udx=0$
Distribute and group us with du and xs with dx.
Then integrate and back sub.
I am sorry I made a clerical error.
$\displaystyle \displaystyle (x+y)\frac{dy}{dx}=y\Rightarrow(x+y)dy=ydx$
$\displaystyle y=ux \ \ \ dy=xdu+udx$
$\displaystyle xdy+ydy=ydx\Rightarrow x(xdu+udx)+ux(xdu+udx)=uxdx$
$\displaystyle x^2du+xudx+ux^2du+u^2xdx=uxdx$
$\displaystyle x^2du+ux^2du+u^2xdx=0\Rightarrow (x^2+ux^2)du=-u^2xdx$
$\displaystyle \displaystyle \frac{1+u}{u^2}du=-\frac{dx}{x}$
Sorry about the mistake earlier. Do you understand now?