this is the problem: xy'' -x(y')^2 = y'
my book says that i need to substitute u=y' and du/dx=y''...
so i get:
x(du/dx)-xu^2 = u
so next the book says i need to separate the x's/dx' to one side and u's/du's to the other. however, i cannot do it
am i using the correct technique...
i must be making a trivial algebraic mistake....as far as i know im supposed to be isolating dx's and x's on one side with u's and du's on the other...which is why i divided through by x. is this not allowed?
oh boy, i see it...i cant get dx to the other side like that...let me see what i...
problem: xy'' -x(y')^2 = y'
what i have so far:
u=y' and du/dx=y''
du/dx - u^2 = (1/x)u
int[(1/u)-u]du = int[1/x]dx
ln u - (1/2)u^2 = ln x +c
ok, now is what ive done so far correct? what do i do next?
ps: i'd like to say hi to everyon :) im new here