Question

dy/dx = (y+8x)/(x+2y)

I know the way to the solution is long therefore if you can please tell me what method are you using for the solution and what is the final answer? tnx :)

Answer 1

btw I used F(y/x)=v(x)

Answer 2

take x common from Nmr. n Dnr. and put y=vx and then replace dy/dx by v+x(dv/dx) and solve accordingly

Answer 3

I've done that, that's where things got ugly

Answer 4

I replaced the dv/dx with dx/dv and isolated the dx/dv on one side minus all the X's
and got a Homogeneous equation for x(v)

Answer 5

btw sry for my lingo, my main language is not English

Answer 6

I got a solution for x(v)
\[x(v)=ce ^{(4-v^2)^(3/8)}\]

Answer 7

u must have got this\[x(dv/dx)=2(4-v^2)/1+2v\]

Answer 8

the main problem is that I'm not sure about my final answer

Answer 9

yep

Answer 10

that's where I changed the equation from v(x) based to x(v) based.
is that what I should have done or is there another way?
because when I'm doing this I'm getting a Homogeneous equation which is easy to solve

Answer 11

after solving u'll get 2+v/(2-v)(4-v^2)^2=x^8c

Answer 12

ok tnx and if I want to get the : y(x) I need to isolate the v annd put it in the first equation - y(x)=x*v(x) ?

Answer 13

oh yes to get final answer put v=y/x. Are u in high school?

Answer 14

lol no

Answer 15

I'm taking a course in Linear differential equation this is from the homework of the second week

Answer 16

solve this one dy/dx= x+3y+2/3x+9y+6

Answer 17

sorry this one dy/dx= x+3y+2/3x+9y+5

Answer 18

dy/dx=1/3
y(x)=1/3*x

Answer 19

ohh that will take me a few minutes

Answer 20

-(3x+9y+5)dy+(x+3y+2)dx=0
from here we need to make it into an exact equation

Answer 21

hey no need for that it can be solve easily

Answer 22

sry this is an exact equation

Answer 23

any way Shiv tnx for the help I need to go to another class :)