Question

Solve this DE: ydx-4(x+y^6)dy=0

Answer 1

the chapter it is in is linear equations but i can't seem to figure out how

Answer 2

i thought in order to do this you had to set it up as

y'+p(x)y=g(x)

however this is p(x,y)

Answer 3

the only ways up to this point were seperation of variables and linear so....

Answer 4

jim do you see a possible way?

Answer 5

would this be like an implicit solution?

Answer 6

\[e^{\int{}{}\frac{1}{-4(x+y^6)}dx} \]

Answer 7

in which you'd make u=-4(x+y^6)=-4x-4y^6

du=-4dx

du/-4=dx?

Answer 8

i don't believe there was an implicit example in the book but that's the only way i can think =/

Answer 9

this was in linear equations sooo i have to write it sa

y' +p(x)y=g(x)=0

\[ydx-4(x+y^6)dy=0\]

divide by dx

\[y-4(x+y^6)y'=0\]

divide both by -4(x+y^6)

\[\frac{1}{-4(x+y^6)}y+y'=0=y'+\frac{1}{-4(x+y^6)}y\]

Answer 10

seems i've stumped everyone .....

Answer 11

I think i might have figured it out

Answer 12

if i divide by dy and then distribute out

Answer 13

i get

\[y\frac{dx}{dy}-4x-4y^6=0\]

add 4y^6

\[y\frac{dx}{dy}-4x=4y^6\]

divide by y

\[\frac{dx}{dy}-\frac{1}{y}x=4y^5\]

Answer 14

am ion the right track by finding the reciprical

Answer 15

and this answer would be implicit to the solution y'

Answer 16

because this equation is linear to the variable y not x


x'+p(y)x=g(y)

Answer 17

i mean it's linear to the variable x not y

Answer 18

\[\frac{y\cdot dx - x\cdot dy}{y}=4y^5dy \implies\frac{y\cdot d(x) - x\cdot d(y)}{y^2}=4y^4dy \]\[\implies d\left(\frac{x}{y}\right) = d\left(\frac{4y^5}{5}\right)\implies \frac{x}{y}= \frac{4y^5}{5} + C\]

Answer 19

Am I right?

Answer 20

not even close

Answer 21

wait let me check

Answer 22

because you wrote the wrong equation :/ check your last post. forgot to carry the four.

Answer 23

it's gotta be linear in aspect to x so i think i have it rightly situated

Answer 24

answer is

\[x=2y^6+cy^4\]

Answer 25

try solving for dx/dy instead ..

Answer 26

solved it and got it right i got a new question with no answer tho so