Question

dy/dx=(y-x)(4x+y)/x(5x-y)

Answer 1

let y = vx
y' = v + v'x

Answer 2

Help me to solve this

Answer 3

i just dd ...

Answer 4

wherever you see a y, replace it by vx

wherever you see a y', replace it by v+v'x

it then becomes seperable

Answer 5

or so ive been lead to assume :)

Answer 6

then i should used dy=vdx+xdv?

Answer 7

What would be the equation looked like? I cannot really understand how. So sorry

Answer 8

dy/dx=(y-x)(4x+y)/x(5x-y)

\[y'=\frac{(y-x)(4x+y)}{x(5x-y)}\]
\[y=vx,~y'=v+v'x\]
\[v+v'x=\frac{(vx-x)(4x+vx)}{x(5x-vx)}\]
\[v+v'x=\frac{xx(v-1)(4+v)}{xx(5-v)}\]
\[\frac{dv}{dx}x=\frac{(v-1)(4+v)}{(5-v)}-v\]
can you see how its going?

Answer 9

why didn't you used the dy=vdx+xdv?

Answer 10

hey? still there?

Answer 11

??

Answer 12

i have my own notation i perfer

Answer 13

\[y=vx\]
\[\frac{d}{dx}y=\frac{d}{dx}vx\]
\[\frac{dy}{dx}=\frac{dv}{dx}x+v\frac{dx}{dx}\]
since dx/dx = 1

\[\frac{dy}{dx}=\frac{dv}{dx}x+v\]
\[dy=x~{dv}+v~dx\]
is fine

Answer 14

its just easier to write it in ' notation is all

Answer 15

\[v'x=\frac{(v-1)(4+v)}{(5-v)}-v\]
\[v'x=\frac{(v-1)(4+v)-v(5-v)}{(5-v)}\]
\[\int\frac{(5-v)}{(v-1)(4+v)-v(5-v)}~dv=\int\frac 1xdx\]
pretty sure they constructed it so that left side simplifies

Answer 16

\[\frac12\int\frac{5-v}{(v-2)(v+1)}dv=ln(x)+C\]
looks like a simple decomp

Answer 17

i just copy your answers but i need to prefer with my notes. i need to study this, our exam is on thurs. thank you! differential equation and mechanics is not easy for me

Answer 18

if you prefer in my notes. does it look like this vdx+xdv/dx=(vx-x)(4x+vx)/x(5x-vx) ?

Answer 19

thats doable yes

Answer 20

then hows next?

Answer 21

factor your xs ... you want to algebra this into 2 seperate function: f(v) and g(x)

Answer 22

can ou show me how?

Answer 23

i already did ....

Answer 24

if you are working on diffy qs, you should already know some basic algebra to manipulate stuff around ...

i got it too:\[\int\frac{(5-v)}{(v-1)(4+v)-v(5-v)}~dv=\int\frac 1xdx\]
which can further be worked (assuming i didnt make an error) to:\[\frac12\int\frac{5-v}{(v-2)(v+1)}dv=\int \frac1x dx\]

Answer 25

used my preference? can you?

Answer 26

you can use your preferences ... either way, it will algebra into that to work on

Answer 27

Thank you. Goodnight maybe i should get slomme sleep. till next time =))

Answer 28

Take care

Answer 29

sweet dreams :)