Question

this is differential equation & linear algebra problem

i know how to do the exact problem but not sure about Not quite exact problems

it tells me to convert to exact equations: multiply x^my^n)
Determine if the equation has an integrating factor u(mu)(x,y)=x^my^n
Find the general solution.

ex: (1-xy)y'+y^2+3xy^3)

Answer 1

\[(1-xy)y'+y^2+3xy^3=0\]\[(y^2+3xy^3)dx+(1-xy)dy=0\]\[Mdx+Ndy=0\]equation is not exact so we must find an integrating factor \(x^my^n\) such that\[\frac{\partial (Mx^my^n)}{\partial y}=\frac{\partial (Nx^my^n)}{\partial x }\]

Answer 2

so setup an equation using the last equality and find m,n

Answer 3

ok i get up to there but what do i do after that?

Answer 4

after that multiplying both sides of equation by \(x^my^n\) u will come up with an exact differential equation and solve it like what u do with exacts

Answer 5

*both sides of original equation

Answer 6

hm... it is still confusing..

Answer 7

why we lookin for integrating factor?

Answer 8

im looking for the general solution. the other part is just determining the integrating factor. Im guessing.

Answer 9

yeah u lookin for integrating factor to make ur equation exact and then go to evaluate general solution...and what is our integrating factor?

Answer 10

i just have u or mu in greek word u(x,y)=x^my^n

Answer 11

well ... its ok

Answer 12

oh nvm i see the formula is x^my^n [ the equation in here] = x^my^n [0]

Answer 13

i will try it out and then report back thanks for all the help =)