Question

Solve the differential equation (2x+7y)dx-(4x-y)dy=0 .... Thanks ! =)

Answer 1

use homogeneous thingies

Answer 2

can you show me how ? and how did you know it's homogenous ?

Answer 3

homogeneous thingies !

Answer 4

it is non Exact differential equation. you will have to find integrating factor to make it exact.

Answer 5

yes. thank you. but can you explain more ? how did you know it's homogenous and how can i solve it ? thanks !

Answer 6

you can use x=tx and y=ty if you can take out t back then it is homogeneous.

Answer 7

@lgbasallote help him .sorry i got a go :(

Answer 8

normally when everything has the same degree it is homogeneous...

Answer 9

andeverything here has degree of 1 so i know it is homogeneous

Answer 10

bye everything i mean all terms

Answer 11

\[(2x+7y)\text dx-(4x-y)\text dy=0\]\[2x+7y\text dx=(4x-y)\text dy\]\[\frac{2x+7y}{4x-y}=\frac{\text dy}{\text dx}\]
\[\frac{\text dy}{\text dx}=\frac{2x+7y}{4x-y}=\frac{2+7\frac yx}{4-\frac yx}\]

let \[\qquad v=\frac yx\qquad y=vx\qquad \frac {\text dy}{\text dx}=v+x\frac{\text dv}{\text dx}\]


\[v+x\frac{\text dv}{\text dx}=\frac{2+7v}{4-v}\]

Answer 12

which is variables separable ,

Answer 13

thank you very very much !!!!