Question

differential equation help?

how do i rearrange this eqn so it can fit the standard form of y' + P(x) y = q(x)

i cant seem to isolate the y's

Answer 1

(1-2x^2-2y) dy/dx = (4x^3 - 4xy)

Answer 2

trying to do : (4x^3 - 4xy) / (1-2x^2-2y)
havve 4x^3 / (1-2x^2-2y) - 4xy/ (1-2x^2-2y)

Answer 3

too many y's

Answer 4

i can't see that this is possible
perhaps another method is required

Answer 5

is there another way to differentiate without finding integrating factor...?

Answer 6

yeah, i think you need to do Integrating factors since My = Nx

Answer 7

... My = Nx...?

and i cant isolate y so i cant get integrating factor...

Answer 8

I may be wrong, but
M(x,y) + N(x,y)*y' = 0
So
M = 4x^3 - 4xy
My = -4x
N = (1-2x^2 - 2y)
Nx = -4x
So there is an exact solution

Answer 9

I'm a little fuzzy on this part, but I believe you do

\[Q = \int\limits_{}^{} M dx \]

and then

\[Q = \int\limits_{}^{} N dy\]

and solve for Q.

But I may have some of my subscripts backwards. I can try and sort it out if this doesn't make sense.

Answer 10

sorry dude, u lost me at My = -4x...?

Answer 11

dM / dy = My
dN/ dx = Nx

Answer 12

ah, cool, back woth u now

Answer 13

If My = Nx, then there is an exact solution

Answer 14

wukk try working through it that way, cheers for that @Xetion

Answer 15

*will try

Answer 16

I got \[x^4 - 2x^2y +y - y^2 =0\]