Question

is it possible to separate this differential equation

dy/dx - ycotx = x

or could the question be wrong?

Answer 1

you might have to employ a different tactic

Answer 2

get it in the form of y/x i believe

Answer 3

then replace it with a "v" or "z"

Answer 4

its not a technique i do enough to recall the details; but i think thats the brunt of it

Answer 5

\[y' = x+ y\ cot(x)\]
\[y' = 1+ \frac{y}{x}\ cot(x)\]
z = y/x

z' = (xy' - x'y) x^2 and solve for y' and sub it in

Answer 6

that make any sense?

Answer 7

\[y' = 1+ \frac{y}{x}\ cot(x)\]
\[z'x +z = 1+ z\ cot(x)\]
\[z'x = 1+ z\ cot(x)-z\]
\[z' = \frac{1+ z\ cot(x)-z}{x}\]
if i remember it right

Answer 8

Yes it makes sense but the question says to solve the differential equation and i'm not sure how introducing z helps?

Answer 9

z is just a substitution for "y/x" to make it easier to seperate and solve

Answer 10

or its spose to :)

Answer 11

i almost had it right :) since z=y/x; then y = zx, and derive for y'

Answer 12

since z is lousy in the font ill use v
\[v=\frac{y}{x}\]
\[y=vx\]
\[y'=v+x\frac{dv}{dx}'\]

Answer 13

heres a good explanation if we can use it:

http://www.youtube.com/watch?v=UpLQUGBznE4&feature=related

Answer 14

Thanks!

Answer 15

youre welcome, hope it helps ..