Question

For the differential equation y(1+xy)dx+x(1-xy)dy=0 , Integrating factor 1/(M

Answer 1

Answer:

I don't know the answer please do me brilliant and follow me please.

Step-by-step explanation:

♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡

Answer 2

Answer:

Step-by-step explanation:

(1+xy)ydx +(1-xy)dy = 0

(ydx+xdy+xy²dx-x²dy = 0) 1/x²y²

∫y dx+xdy/x²y²  + ∫dx/x - ∫dy/y = 0 = C

-1/xy + log x -log y = c

-1/xy + log (x/y) = c

log (x/y ) - 1/xy = c

Integrating factor :

In maths , an integrating factor is a function used to solve differential equations .It is an function in which an ordinary differential equation can be multiplied to make the function integrable .it is usually applied to solve ordinary differential equation also , we can use this factor   within multivariable calculus when multiplied by an integrating factor , an inaccurate differential made into an accurate differential (which can be later integrated to give a scalar field ) It has a major application in thermodynamics where the temperature becomes the integrating factor that makes entropy an exact differential .

Integrating factor is defined as the function which is selected in order to solve the given differential equation .It is most commonly used in ordinary linear differential equations of the first order.

when the given differential equation is not the form

dy/dx +p(x)y = Q(x)

then the integrating factor is defined as :

 μ = e^∫p(x)dx